Electromagnetic Theory Multiple Choice Questions

Electromagnetic Theory Questions and Answers
Dot and Cross Product
1. When two vectors are perpendicular, their
a) Dot product is zero b) Cross product is zero c) Both are zero
d) Both are not necessarily zero
Answer: a
Explanation: Dot product of two perpendicular vectors is given by A.B = |a||b|cos 90, which is zero.
Thus, dot product is zero and vectors are perpendicular.
2. The cross product of the vectors 3i + 4j – 5k and –i + j – 2k is,
a) 3i – 11j + 7k b) -3i + 11j + 7k
c) -3i – 11j – 7k d) -3i + 11j – 7k
Answer: b
Explanation: Cross product of two vectors is,
A X B = (a2*b3 – b2*a3)i – (a1*b3 – b1*a3)j + (a1*b2 – b1*a2)k.
Using the formula, the answer can be calculated.
3. Which of the following are not vector functions in Electromagnetic?
a) Gradient b) Divergence
c) Curl d) There is no non- vector functions in Electromagnetics
Answer: d
Explanation: Since all the coordinates in electromagnetic are space coordinates, direction and magnitude
both are important. Thus all functions are vector only.
4. The work done of vectors force F and distance d, separated by angle θ can be calculated using,
a) Cross product b) Dot product
c) Addition of two vectors d) Cannot be calculated
www.studymaterialz.in

Answer: b
Explanation: Force is a vector quantity, whereas distance is scalar. Work is defined as the product of
force and distance, which is given by dot product.
5. Find whether the vectors are parallel, (-2,1,-1) and (0,3,1)
a) Parallel b) Collinearly parallel
c) Not parallel d) Data insufficient
Answer: c
Explanation: Two vectors are parallel when their cross product is zero. Since their cross product is 4i +
2j – 6k (non-zero), the vectors are not parallel.
6. Lorentz force is based on,
a) Dot product b) Cross product
c) Both dot and cross product d) Independent of both
Answer: b
Explanation: Lorentz force is given by, F = q (v x B).Thus cross product is the answer.
7. Electromagnetic forces are defined by
a) Fleming’s right hand rule b) Fleming’s left hand rule
c) Faraday’s law d) Ampere law
Answer: b
Explanation: The three left hand fingers denote electric field, magnetic field and wave propagation in
free space, analogous to force, magnetic field and current respectively in any conductor.
8. The dot product of two vectors is a scalar. The cross product of two vectors is a vector. State
True/False.
a) True b) False
Answer: a
Explanation: Dot product is an algebraic operation that takes two equal length sequences and returns a
scalar. Cross product is a binary operation that calculates area of two vectors, thus vector quantity.
9. Which of the Pythagorean Theorem is valid in Electromagnetics?
a) |dot product| + |dot product| = 1 b) |cross product| – |cross product| = 1
c) |dot product|2
+ |cross product|2
= 1 d) |dot product| + |cross product| = 0
Answer: c
Explanation: Option c gives |cos|2
+ |sin|2
= 1, which is the right answer.

10. Which of the following is not true?
a) A . (B . C) = scalar value b) A . (B x C) = scalar value
c) A x (B . C) = scalar value d) A x (B x C) = vector value
Answer: c
Explanation: Cross product of dot product of two vectors is a vector value.
“Position and Distance Vectors”.
1. The distance vector is obtained in
a) Cartesian coordinate system b) Spherical coordinate system
c) Circular coordinate system d) Space coordinate system
Answer: d
Explanation: Vector formed by connecting two points in space is distance vector. Thus, it
is obtained in space coordinate system.
2. The divergence of distance vector is
a) 0 b) 3 c) 2 d) 1
Answer: b
Explanation: The distance vector of any coordinates is generally, r = xi + yj + zk. The
divergence of r is 1 + 1 + 1 = 3.
3. Find a vector normal to a plane consisting of points p1(0,1,0), p2(1,0,1) and
p3(0,0,1)
a) –j – k b) –i – j c) –i – k d) –i – j – k
Answer: a
Explanation: Distance vector from p1 and p2 is a = i – j + k. Distance vector from p1
and p3 is b = –j + k. The vector normal to these points is a X b = -j – k.
4. The unit vector to the points p1(0,1,0), p2(1,0,1), p3(0,0,1) is
a) (-j – k)/1.414 b) (-i – k)/1.414

c) (-i – j)/1.414 d) (-i – j – k)/1.414
Answer: a
Explanation: The cross product of p1, p2, p3 is a X b = -j – k and its magnitude is 1.414.
The unit normal vector is given by, (-j –k)/1.414.
5. The polar form of Cartesian coordinates is
a) Circular coordinates b) Spherical coordinates
c) Cartesian coordinates d) Space coordinates
Answer: a
Explanation: The radius in the polar coordinates is the Pythagorean triplet-(r,x,y).Thus it
is the circular coordinates.
6. The work-electric field relation is given by
a) Volume integral
b) Surface integral
c) Line integral
d) Relation impossible
Answer: c
Explanation: The work done is given by, W = -Q ∫E dl. Thus it is line integral.
7. The distance vector can be used to compute which of the following?
a) Dot product
b) Cross product
c) Unit normal vector
d) Area
Answer: c
Explanation: The distance vector is the distance between two points on space, thus the
unit normal vector is computed using the distance vector.
8. Distance and position vectors rely on field strength. State True/False.
a) True

b) False
Answer: a
Explanation: Position or distance of a vector is dependent on the field strength.
9. Find the projection of A on B. Given A = 10j + 3k and B = 4j + 5k.
a) 6
b) 6.25
c) 6.5
d) 6.75
Answer: b
Explanation: Projection of A on B = (A . B)/|B|. Thus the answer is 40/6.4= 6.25.
10. The vector product of two vectors is given by area of the parallelogram. State
True/False.
a) True
b) False
Answer: a
Explanation: The vector product of two vectors is A X B = AB sin θ. n, where n is
the unit normal vector to the plane given by A and B. Their magnitude is given by
|A X B|, which is the area of parallelogram.
Vector Properties
This set of Electromagnetic Theory Multiple Choice Questions & Answers (MCQs)
focuses on “Vector Properties”.
1. The del operator is called as
a) Gradient
b) Curl
c) Divergence

d) Vector differential operator
View Answer
Answer: d
Explanation: The Del operator is used to replace the differential terms, thus called vector
differential operator in electromagnetics.
2. The relation between vector potential and field strength is given by
a) Gradient
b) Divergence
c) Curl
d) Del operator
View Answer
Answer: a
Explanation: The vector potential and field is given by, E = -Del (V).
3. The Laplacian operator is actually
a) Grad(Div V)
b) Div(Grad V)
c) Curl(Div V)
d) Div(Curl V)
View Answer
Answer: b
Explanation: The Laplacian operator is the divergence of gradient of a vector, which is
also called del2
V operator.
4. The divergence of curl of a vector is zero. State True or False.
a) True
b) False
View Answer

Answer: a
Explanation: The curl of a vector is the circular flow of flux. The divergence of circular
flow is considered to be zero.
5. The curl of gradient of a vector is non-zero. State True or False.
a) True
b) False
View Answer
Answer: b
Explanation: The differential flow of flux in a vector is a vector. The curl of this quantity
will be zero.
6. Identify the correct vector identity.
a) i . i = j . j = k . k = 0
b) i X j = j X k = k X i = 1
c) Div (u X v) = v . Curl(u) – u . Curl(v)
d) i . j = j . k = k . i = 1
View Answer
Answer: c
Explanation: By standard proof, Div (u X v) = v . Curl(u) – u . Curl (v).
7. A vector is said to be solenoidal when its
a) Divergence is zero
b) Divergence is unity
c) Curl is zero
d) Curl is unity
View Answer
Answer: a
Explanation: When the divergence of a vector is zero, it is said to be solenoidal
/divergent-free.

8. The magnetic field intensity is said to be
a) Divergent
b) Curl free
c) Solenoidal
d) Rotational
View Answer
Answer: c
Explanation: By Maxwell’s equation, the magnetic field intensity is solenoidal due to the
absence of magnetic monopoles.
9. A field has zero divergence and it has curls. The field is said to be
a) Divergent, rotational
b) Solenoidal, rotational
c) Solenoidal, irrotational
d) Divergent, irrotational
View Answer
Answer: b
Explanation: Since the path is not divergent, it is solenoidal and the path has curl, thus
rotational.
10. When a vector is irrotational, which condition holds good?
a) Stoke’s theorem gives non-zero value
b) Stoke’s theorem gives zero value
c) Divergence theorem is invalid
d) Divergence theorem is valid
View Answer
Answer: b
Explanation: Stoke’ theorem is given by, ∫ A.dl = ∫ (Curl A). ds, when curl is
zero(irrotational), the theorem gives zero value.

Cartesian Coordinate System
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focuses on “Cylindrical Coordinate System”.
1. The Cartesian system is also called as
a) Circular coordinate system
b) Rectangular coordinate system
c) Spherical coordinate system
d) Space coordinate system
View Answer
Answer: b
Explanation: The other name for Cartesian is rectangular system, which is given by
(x,y,z).
2. The volume of a parallelepiped in Cartesian is
a) dV = dx dy dz
b) dV = dx dy
c) dV = dy dz
d) dV = dx dz
View Answer

Answer: a
Explanation: The volume of a parallelepiped is given by product of differential length,
breadth and height.
3. A charge is placed in a square container. The position of the charge with respect to the
origin can be found by
a) Spherical system
b) Circular system
c) Cartesian system
d) Space coordinate system
View Answer
Answer: c
Explanation: Since the container possesses dimensions of a square (length, breadth and
height), it can be found by Cartesian system.
4. The scalar factor of Cartesian system is unity. State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: The range of Cartesian system is one to infinity. Thus the minimum scalar
value of the system is unity.
5. The angular separation between the vectors A = 4i + 3j + 5k and B = i – 2j + 2k is (in
degrees)
a) 65.8
b) 66.8
c) 67.8
d) 68.8
View Answer

Answer: c
Explanation: The dot product the vector is 8. Angle of separation is cos θ = 8/ (7.07 X 3)
= 0.377 and θ = cos-1
(0.377) = 67.8.
6. The Cartesian coordinates can be related to cylindrical coordinates and spherical
coordinates. State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: All the coordinate systems are inter-convertible and all the vector operations
are applicable to it.
7. Transform the vector A = 3i – 2j – 4k at P(2,3,3) to cylindrical coordinates
a) -3.6j – 4k
b) -3.6j + 4k
c) 3.6j – 4k
d) 3.6j + 4k
View Answer
Answer: a
Explanation: Convert the Cartesian form to cylindrical form by formula and substitute the
points to get -3.6j – 4k.
8. The spherical equivalent of the vector B = yi + (x + z)j located at (-2,6,3) is given by
a) (7,64.62,71.57)
b) (7,-64.62,-71.57)
c) (7,-64.62,71.57)
d) (7,64.62,-71.57)
View Answer

Answer: d
Explanation: Substitute the points in the vector and convert the Cartesian to cylindrical
form to get radius as 7, plane angle1 as 64.62 and plane angle2 as -71.57.
9. Which of the following criteria is used to choose a coordinate system?
a) Distance
b) Intensity
c) Magnitude
d) Geometry
View Answer
Answer: d
Explanation: The coordinate system is chosen based on the geometry of the given
problem. From a point charge +Q, the electric field spreads in all 360 degrees. The
calculation of electric field in this case will be spherical system.
10. Vector transformation followed by coordinate point substitution and vice-versa, both
given the same result. Choose the best answer.
a) Possible, when the vector is constant
b) Possible, when the vector is variable
c) Possible in all cases
d) Not possible
View Answer
Answer: a
Explanation: The order of vector transformation and point substitution will not affect the
result, only when the vector is a constant.
Cylindrical Coordinate System
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focuses on “Spherical Coordinate System”.
1. The cylindrical coordinate system is also referred to as
a) Cartesian system
b) Circular system
c) Spherical system
d) Space system
View Answer
Answer: b
Explanation: The cylindrical coordinates(r,φ,z) is also called as circular system and is
used for systems with circular dimensions.
2. Transform the vector B=yi+(x+z)j located at point (-2,6,3) into cylindrical coordinates.
a) (6.325,-71.57,3)
b) (6.325,71.57,3)
c) (6.325,73.57,3)
d) (6.325,-73.57,3)
View Answer
Answer: a
Explanation: ρ = √(x2
+y2
) = √40 = 6.325
Φ = tan-1
(y/x) = tan-1
(-6/2) = -71.57
z = 3.
3. Cylindrical systems have the following scalar values respectively
a) 1, ρ ,1
b) 1, 1, 1
c) 0,1,0
d) 1,0,0
View Answer

Answer: a
Explanation: The range of radius is one to unity, that of plane angle is one to 360 degree
and that of z plane is one to infinity. Thus the minimum scalar factor has to be 1, ρ , 1.
4. A charge located at point p (5,30⁰,2) is said to be in which coordinate system?
a) Cartesian system
b) Cylindrical system
c) Spherical system
d) Space system
View Answer
Answer: b
Explanation: The cylindrical system is of the form (ρ, φ, z), which relates the point given
in the question.
5. Cylindrical system is employed in waveguides. State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: Cylindrical systems are employed in circular waveguides, whereas
Cartesian systems are employed in rectangular waveguides.
6. The pressure inside a piston cylinder is a variable of
a) Radius
b) Plane angle
c) Z plane distance
d) Constant, not a variable
View Answer

Answer: c
Explanation: Pressure varies up and down in a cylinder due to suction. Thus it is
dependent on the z plane distance of the cylinder.
7. Charges filled inside a cylindrical will possess flux in which direction?
a) Upwards
b) Downwards
c) Laterally outwards
d) Inwards
View Answer
Answer: c
Explanation: The flux due to the charges will act outside the cylinder. Since the cylinder
possesses curved surfaces, it will flow laterally outwards.
8. Rectangular waveguides dominate the circular waveguides. Find the reason.
a) Low cut-off frequency
b) Easy to design
c) More wave propagation
d) The statement is false
View Answer
Answer: b
Explanation: Due to linear design, the desired dimensions can be easily constructed using
rectangular waveguides than circular ones.
9. Transform the spherical system B = (10/r)i + (10cos θ)j + k into cylindrical form at (5,
π/2, -2)
a) 2.467i + j + 1.167k
b) 2.467i – j + 1.167k
c) 2.467i – j – 1.167k

d) 2.467i + j – 1.167k
View Answer
Answer: a
Explanation: The equivalent cylindrical form is given by,
B = (10sin θ/r + rcos2θ)i + j + (10cos θ/r –r sin θ cos θ)k
At (5, π/2, -2), r = √(52
+-22
) = √29
sin θ = 5/√29 and cos θ = -2/√29
Thus, B = 2.467i + j + 1.167k.
10. Convert the given rectangular coordinates A(2,3,1) into corresponding cylindrical
coordinates
a) (3.21,56.31,1)
b) (3.21,57.31,0)
c) (3.61,57.31,0)
d) (3.61,56.31,1)
View Answer
Answer: d
Explanation: ρ = √(x2
+y2
) = √13 = 3.61
Φ = tan-1
(y/x) = 56.31
z = 1
Thus, A = (3.61,56.31,1).
Spherical Coordinate System
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This set of Electromagnetic Theory Multiple Choice Questions & Answers focuses on
“Spherical Coordinate System”.

1. Convert the point (3,4,5) from Cartesian to spherical coordinates
a) (7.07,45⁰,53⁰)
b) (0.707,45⁰,53⁰)
c) (7.07,54⁰,63⁰)
d) (0.707,54⁰,63⁰)
View Answer
Answer: a
Explanation: r = √(x2
+y2
+z2
) = √50 = 7.07
Θ = cos-1
(z/r) = cos-1
(5/5√2) = 45⁰
Φ = tan-1
(y/x) = tan-1
(4/3) = 53⁰.
2. Example of spherical system in the following is
a) Charge in space
b) Charge in box
c) Charge in dielectric
d) Uncharged system
View Answer
Answer: a
Explanation: From a point charge +Q, the electric field spreads in all 360 degrees. The
calculation of electric field in this case will be spherical system. Thus it is charge in the
space.
3. Spherical systems are employed in waveguides. State True/False
a) True
b) False
View Answer
Answer: b
Explanation: There is no waveguide designed spherically to avoid absorption, rather than
propagation.

4. Choose which of following condition is not required for a waveguide to exist.
a) The dimensions should be in accordance with desired frequency
b) Cut-off frequency should be minimum 6GHz
c) The shape should be spherical
d) No specific condition is required for waveguide design
View Answer
Answer: c
Explanation: A waveguide need not be spherical, it has to be rectangular or circular, as it
violates the propagation of the wave.
5. Find the spherical coordinates of A(2,3,-1)
a) (3.74, 105.5⁰, 56.13⁰)
b) (3.74, 105.5⁰, 56.31⁰)
c) (3.74, 106.5⁰, 56.13⁰)
d) (3.74, 106.5⁰, 56.31⁰)
View Answer
Answer: b
+y2
+z2
) = √14 = 3.74
Θ = cos-1
(z/r) = cos-1
(-1/3.74) = 105.5⁰
Φ = tan-1
(y/x) = tan-1
(3/2) = 56.31⁰.
6. Find the Cartesian coordinates of B(4,25⁰,120⁰)
a) (0.845, 1.462, 3.625)
b) (-0.845, 1.462, 3.625)
c) (-8.45, 2.462, 6.325)
d) (8.45, 2.462, 6.325)
View Answer
Answer: b
Explanation: x = r sin θ cos φ = 4 sin25⁰ cos 120⁰ = -0.845

y = r sin θ sin φ = 4 sin 25⁰ sin 120⁰ = 1.462
z = r cos θ = 4 cos 25⁰ = 3.625.
7. The area of sphere can be computed from the sphere volume. State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: On double integrating the differential volume, the area can be computed for
a sphere.
8. Given B= (10/r)i+( rcos θ) j+k in spherical coordinates. Find Cartesian points at (-
3,4,0)
a) -2i + j
b) 2i + k
c) i + 2j
d) –i – 2k
View Answer
Answer: a
+y2
+z2
) = √25 = 5
Θ = cos-1
(z/r) = 1
Φ = tan-1
(y/x) = tan-1
(-4/3)
Thus, B = -2i + j.
9. The scalar factor of spherical coordinates is
a) 1, r, r sin θ
b) 1, r, r
c) r, r, 1
d) r, 1, r
View Answer

Answer: a
Explanation: The radius varies from unity to infinity, the plane angle from zero to 360 ⁰
and the z plane from (-∞, ∞) .
10. Transform the vector (4,-2,-4) at (1,2,3) into spherical coordinates.
a) 3.197i – 2.393j + 4.472k
b) -3.197i + 2.393j – 4.472k
c) 3.197i + 2.393j + 4.472k
d) -3.197i – 2.393j – 4.472k
View Answer
Answer: b
+y2
+z2
) = 3.74
Θ = cos-1
(z/r) = cos-1
(3/3.74) = 36.7⁰
Φ = tan-1
(y/x) = tan-1
(2/1) = 63.4⁰
A = (4 sin θ cos φ – 2 sin θ sin φ – 4cos θ)i + (4 cos θ cos φ – 2 cos θ sin φ + 4 sin θ)j + (-
4 sin φ – 2 cos φ)k
On substituting r, θ, φ, A = -3.197i + 2.393j – 4.472k.
Gradient
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focuses on “Gradient”.
1. Gradient of a function is a constant. State True/False.
a) True
b) False
View Answer

Answer: b
Explanation: Gradient of any scalar function may be defined as a vector. The vector’s
magnitude and direction are those of the maximum space rate of change of φ.
2. The mathematical perception of the gradient is said to be
a) Tangent
b) Chord
c) Slope
d) Arc
View Answer
Answer: c
Explanation: The gradient is the rate of change of space of flux in electromagnetics. This
is analogous to the slope in mathematics.
3. Divergence of gradient of a vector function is equivalent to
a) Laplacian operation
b) Curl operation
c) Double gradient operation
d) Null vector
View Answer
Answer: a
Explanation: Div (Grad V) = (Del)2
V, which is the Laplacian operation. A function is
said to be harmonic in nature, when its Laplacian tends to zero.
4. The gradient of xi + yj + zk is
a) 0
b) 1
c) 2
d) 3
View Answer

Answer: d
Explanation: Grad (xi + yj + zk) = 1 + 1 + 1 = 3. In other words, the gradient of any
position vector is 3.
5. Find the gradient of t = x2
y+ ez
at the point p(1,5,-2)
a) i + 10j + 0.135k
b) 10i + j + 0.135k
c) i + 0.135j + 10k
d) 10i + 0.135j + k
View Answer
Answer: b
Explanation: Grad(t) = 2xy i + x2
j + ez
k. On substituting p(1,5,-2), we get 10i + j +
0.135k.
6. Curl of gradient of a vector is
a) Unity
b) Zero
c) Null vector
d) Depends on the constants of the vector
View Answer
Answer: c
Explanation: Gradient of any function leads to a vector. Similarly curl of that vector gives
another vector, which is always zero for all constants of the vector. A zero value in vector
is always termed as null vector(not simply a zero).
7. Find the gradient of the function given by, x2
+ y2
+ z2
at (1,1,1)
a) i + j + k
b) 2i + 2j + 2k
c) 2xi + 2yj + 2zk

d) 4xi + 2yj + 4zk
View Answer
Answer: b
Explanation: Grad(x2
+y2
+z2
) = 2xi + 2yj + 2zk. Put x=1, y=1, z=1, the gradient will be 2i
+ 2j + 2k.
8. The gradient can be replaced by which of the following?
a) Maxwell equation
b) Volume integral
c) Differential equation
d) Surface integral
View Answer
Answer: c
Explanation: Since gradient is the maximum space rate of change of flux, it can be
replaced by differential equations.
9. When gradient of a function is zero, the function lies parallel to the x-axis. State
True/False.
a) True
b) False
View Answer
Answer: a
Explanation: Gradient of a function is zero implies slope is zero. When slope is zero, the
function will be parallel to x-axis or y value is constant.
10. Find the gradient of the function sin x + cos y.
a) cos x i – sin y j
b) cos x i + sin y j
c) sin x i – cos y j

d) sin x i + cos y j
View Answer
Answer: a
Explanation: Grad (sin x + cos y) gives partial differentiation of sin x+ cos y with respect
to x and partial differentiation of sin x + cos y with respect to y and similarly with respect
to z. This gives cos x i – sin y j + 0 k = cos x i – sin y j.
Divergence
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focuses on “Divergence”.
1. The divergence of a vector is a scalar. State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: Divergence can be computed only for a vector. Since it is the measure of
outward flow of flux from a small closed surface as the volume shrinks to zero, the result
will be directionless (scalar).
2. The divergence concept can be illustrated using Pascal’s law. State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: Consider the illustration of Pascal’s law, wherein a ball is pricked with
holes all over its body. After water is filled in it and pressure is applied on it, the water

flows out the holes uniformly. This is analogous to the flux flowing outside a closed
surface as the volume reduces.
3. Compute the divergence of the vector xi + yj + zk.
a) 0
b) 1
c) 2
d) 3
View Answer
Answer: d
Explanation: The vector given is a position vector. The divergence of any position vector
is always 3.
4. Find the divergence of the vector yi + zj + xk.
a) -1
b) 0
c) 1
d) 3
View Answer
Answer: b
Explanation: Div (yi + zj + xk) = Dx(y) + Dy(z) + Dz(x), which is zero. Here D refers to
partial differentiation.
5. Given D = e-x
sin y i – e-x
cos y j
Find divergence of D.
a) 3
b) 2
c) 1
d) 0
View Answer

Answer: d
Explanation: Div (D) = Dx(e-x
sin y) + Dy(-e-x
cos y ) = -e-x
sin y + e-x
sin y = 0.
6. Find the divergence of the vector F= xe-x
i + y j – xz k
a) (1 – x)(1 + e-x
)
b) (x – 1)(1 + e-x
)
c) (1 – x)(1 – e)
d) (x – 1)(1 – e)
View Answer
Answer: a
Explanation: Div(F) = Dx(xe-x
) + Dy(y)+Dz(-xz) = -xe-x
+ e-x
+ 1 – x =
e-x
(1 – x) + (1 – x) = (1 – x)(1 + e-x
).
7. Determine the divergence of F = 30 i + 2xy j + 5xz2
k at (1,1,-0.2) and state the nature
of the field.
a) 1, solenoidal
b) 0, solenoidal
c) 1, divergent
d) 0, divergent
View Answer
Answer: b
Explanation: Div(F) = Dx(30) + Dy(2xy) + Dz(5xz2
) = 0 + 2x + 10xz = 2x + 10xz
Divergence at (1,1,-0.2) will give zero. As the divergence is zero, field is solenoidal.
Alternate/Shortcut: Without calculation, we can easily choose option b, as by theory
when the divergence is zero, the vector is solenoidal. Option b is the only one which is
satisfying this condition.
8. Find whether the vector is solenoidal, E = yz i + xz j + xy k
a) Yes, solenoidal
b) No, non-solenoidal

c) Solenoidal with negative divergence
d) Variable divergence
View Answer
Answer: a
Explanation: Div(E) = Dx(yz) + Dy(xz) + Dz(xy) = 0. The divergence is zero, thus vector
is divergentless or solenoidal.
9. Find the divergence of the field, P = x2
yz i + xz k
a) xyz + 2x
b) 2xyz + x
c) xyz + 2z
d) 2xyz + z
View Answer
Answer: b
Explanation: Div(P) = Dx(x2
yz) + Dy(0) + Dz(xz) = 2xyz + x, which is option b. For
different values of x,y,z the divergence of the field varies.
10. Identify the nature of the field, if the divergence is zero and curl is also zero.
a) Solenoidal, irrotational
b) Divergent, rotational
c) Solenoidal, irrotational
d) Divergent, rotational
View Answer
Answer: c
Explanation: Since the vector field does not diverge (moves in a straight path), the
divergence is zero. Also, the path does not possess any curls, so the field is irrotational.
“Curl”.

1. Curl is defined as the angular velocity at every point of the vector field. State
True/False.
a) True
b) False
View Answer
Answer: a
Explanation: Curl is defined as the circulation of a vector per unit area. It is the cross
product of the del operator and any vector field. Circulation implies the angular at every
point of the vector field. It is obtained by multiplying the component of the vector
parallel to the specified closed path at each point along it, by the differential path length
and summing the results.
2. The curl of curl of a vector is given by,
a) Div(Grad V) – (Del)2
V
b) Grad(Div V) – (Del)2
V
c) (Del)2
V – Div(Grad V)
d) (Del)2
V – Grad(Div V)
View Answer
Answer: b
Explanation: Curl (Curl V) = Grad (Div V) – (Del)2
V is a standard result of the curl
operation.
3. Which of the following theorem use the curl operation?
a) Green’s theorem
b) Gauss Divergence theorem
c) Stoke’s theorem
d) Maxwell equation
View Answer
4. The curl of a curl of a vector gives a
a) Scalar

b) Vector
c) Zero value
d) Non zero value
View Answer
Answer: b
Explanation: Curl is always defined for vectors only. The curl of a vector is a vector only.
The curl of the resultant vector is also a vector only.
5. Find the curl of the vector and state its nature at (1,1,-0.2)
F = 30 i + 2xy j + 5xz2
k
a) √4.01
b) √4.02
c) √4.03
d) √4.04
View Answer
Answer: d
Explanation: Curl F = -5z2
j + 2y k. At (1,1,-0.2), Curl F = -0.2 j + 2 k. |Curl F| = √(-
0.22
+22
) = √4.04.
6. Is the vector is irrotational. E = yz i + xz j + xy k
a) Yes
b) No
View Answer
Answer: a
Explanation: Curl E = i(Dy(xy) – Dz(xz)) – j (Dx(xy) – Dz(yz)) + k(Dx(xz) – Dy(yz)) =
i(x – x) – j(y – y) + k(z – z) = 0
Since the curl is zero, the vector is irrotational or curl-free.
7. Find the curl of A = (y cos ax)i + (y + ex
)k
a) 2i – ex j – cos ax k

b) i – ex j – cos ax k
c) 2i – ex j + cos ax k
d) i – ex j + cos ax k
View Answer
Answer: b
Explanation: Curl A = i(Dy(y + ex)) – j (Dx(y + ex) – Dz(y cos ax)) + k(-Dy(y cos ax))
= 1.i – j(ex) – k cos ax = i – ex j – cos ax k.
8. Find the curl of the vector A = yz i + 4xy j + y k
a) xi + j + (4y – z)k
b) xi + yj + (z – 4y)k
c) i + j + (4y – z)k
d) i + yj + (4y – z)k
View Answer
Answer: d
Explanation: Curl A = i(Dy(y) – Dz(0)) – j (Dx(0) – Dz(yz)) + k(Dx(4xy) – Dy(yz)) =
i + y j + (4y – z)k, which is option d.
9. Curl cannot be employed in which one of the following?
a) Directional coupler
b) Magic Tee
c) Isolator and Terminator
d) Waveguides
View Answer
Answer: d
Explanation: In the options a, b, c, the EM waves travel both in linear and angular
motion, which involves curl too. But in waveguides, as the name suggests, only guided
propagation occurs (no bending or curl of waves).

10. Which of the following Maxwell equations use curl operation?
a) Maxwell 1st and 2nd equation
b) Maxwell 3rd and 4th equation
c) All the four equations
d) None of the equations
View Answer
Answer: a
Explanation: Maxwell 1st equation, Curl (H) = J (Ampere law)
Maxwell 2nd equation, Curl (E) = -D(B)/Dt (Faraday’s law)
Maxwell 3rd equation, Div (D) = Q (Gauss law for electric field)
Maxwell 4th equation, Div (B) = 0(Gauss law for magnetic field)
It is clear that only 1st and 2nd equations use the curl operation.
“Line Integral”.
1. An electric field is given as E = 6y2
z i + 12xyz j + 6xy2
k. An incremental path is given
by dl = -3 i + 5 j – 2 k mm. The work done in moving a 2mC charge along the path if the
location of the path is at p(0,2,5) is (in Joule)
a) 0.64
b) 0.72
c) 0.78
d) 0.80
View Answer
Answer: b
Explanation: W = -Q E.dl
W = -2 X 10-3
X (6y2
z i + 12xyz j + 6xy2
k) . (-3 i + 5 j -2 k)
At p(0,2,5), W = -2(-18.22.5) X 10-3
= 0.72 J.

2. The integral form of potential and field relation is given by line integral. State
True/False
a) True
b) False
View Answer
Answer: a
Explanation: Vab = -∫ E.dl is the relation between potential and field. It is clear that it is
given by line integral.
3. If V = 2x2
y – 5z, find its electric field at point (-4,3,6)
a) 47.905
b) 57.905
c) 67.905
d) 77.905
View Answer
Answer: b
Explanation: E = -Grad (V) = -4xy i – 2×2 j + 5k
At (-4,3,6), E = 48 i – 32 j + 5 k, |E| = √3353 = 57.905 units.
4. Find the potential between two points p(1,-1,0) and q(2,1,3) with E = 40xy i + 20x2
j +
2 k
a) 104
b) 105
c) 106
d) 107
View Answer
Answer: c
Explanation: V = -∫ E.dl = -∫ (40xy dx + 20x2
dy + 2 dz) , from q to p.
On integrating, we get 106 volts.

5. Find the potential between a(-7,2,1) and b(4,1,2). Given E = (-6y/x2
)i + ( 6/x) j + 5 k.
a) -8.014
b) -8.114
c) -8.214
d) -8.314
View Answer
Answer: c
Explanation: V = -∫ E.dl = -∫ (-6y/x2 )dx + ( 6/x)dy + 5 dz, from b to a.
On integrating, we get -8.214 volts.
6. The potential of a uniformly charged line with density λ is given by,
λ/(2πε) ln(b/a). State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: The electric field intensity is given by, E = λ/(2πεr)
Vab = -∫ E.dr = -∫ λ/(2πεr). On integrating from b to a, we get λ/(2πε) ln(b/a).
7. A field in which a test charge around any closed surface in static path is zero is called
a) Solenoidal
b) Rotational
c) Irrotational
d) Conservative
View Answer
Answer: d
Explanation: Work done in moving a charge in a closed path is zero. It is expressed as, ∫
E.dl = 0. The field having this property is called conservative or lamellar field.

8. The potential in a lamellar field is
a) 1
b) 0
c) -1
d) ∞
View Answer
Answer: b
Explanation: Work done in a lamellar field is zero. ∫ E.dl = 0,thus ∑V = 0. The potential
will be zero.
9. Line integral is used to calculate
a) Force
b) Area
c) Volume
d) Length
View Answer
Answer: d
Explanation: Length is a linear quantity, whereas area is two dimensional and volume is
three dimensional. Thus single or line integral can be used to find length in general.
10. The energy stored in the inductor 100mH with a current of 2A is
a) 0.2
b) 0.4
c) 0.6
d) 0.8
View Answer
Answer: a
Explanation: dw = ei dt = Li di, W = L∫ i.di
Energy E = 0.5LI2
= 0.5 X 0.1 X 22
= 0.2 Joule.

“Surface Integral”.
1. Gauss law for electric field uses surface integral. State True/False
a) True
b) False
View Answer
Answer: a
Explanation: Gauss law states that the electric flux passing through any closed surface is
equal to the total charge enclosed by the surface. Thus the charge is defined as a surface
integral.
2. Surface integral is used to compute
a) Surface
b) Area
c) Volume
d) density
View Answer
Answer: b
Explanation: Surface integral is used to compute area, which is the product of two
quantities length and breadth. Thus it is two dimensional integral.
3. Coulomb’s law can be derived from Gauss law. State True/ False
a) True
b) False
View Answer
Answer: a
Explanation: Gauss law, Q = ∫∫D.ds
By considering area of a sphere, ds = r2
sin θ dθ dφ.
On integrating, we get Q = 4πr2
D and D = εE, where E = F/Q.
Thus, we get Coulomb’s law F = Q1 x Q2/4∏εR2
.

4. Evaluate Gauss law for D = 5r2
/4 i in spherical coordinates with r = 4m and θ = π/2.
a) 600
b) 599.8
c) 588.9
d) 577.8
View Answer
Answer: c
Explanation: ∫∫ ( 5r2
/4) . (r2
sin θ dθ dφ), which is the integral to be evaluated.
Put r = 4m and substitute θ = 0→ π/4 and φ = 0→ 2π, the integral evaluates to 588.9.
5. Compute the Gauss law for D= 10ρ3
/4 i, in cylindrical coordinates with ρ= 4m, z=0
and z=5.
a) 6100 π
b) 6200 π
c) 6300 π
d) 6400 π
View Answer
Answer: d
Explanation: ∫∫ D.ds = ∫∫ (10ρ3
/4).(ρ dφ dz), which is the integral to be evaluated. Put ρ =
4m, z = 0→5 and φ = 0→2π, the integral evaluates to 6400π.
6. Compute divergence theorem for D= 5r2
/4 i in spherical coordinates between r=1 and
r=2.
a) 80π
b) 5π
c) 75π
d) 85π
View Answer
Answer: c
Explanation: ∫∫ ( 5r2
/4) . (r2
sin θ dθ dφ), which is the integral to be evaluated. Since it is

double integral, we need to keep only two variables and one constant compulsorily.
Evaluate it as two integrals keeping r = 1 for the first integral and r = 2 for the second
integral, with φ = 0→2π and θ = 0→ π. The first integral value is 80π, whereas second
integral gives -5π. On summing both integrals, we get 75π.
7. Find the value of divergence theorem for A = xy2
i + y3
j + y2
z k for a cuboid given by
0<x<1, 0<y<1 and 0<z<1.
a) 1
b) 4/3
c) 5/3
d) 2
View Answer
Answer: c
Explanation: A cuboid has six faces. ∫∫A.ds = ∫∫Ax=0 dy dz + ∫∫Ax=1 dy dz + ∫∫Ay=0 dx
dz + ∫∫Ay=1 dx dz + ∫∫Az=0 dy dx + ∫∫Az=1 dy dx. Substituting A and integrating we get
(1/3) + 1 + (1/3) = 5/3.
8. The ultimate result of the divergence theorem evaluates which one of the following?
a) Field intensity
b) Field density
c) Potential
d) Charge and flux
View Answer
Answer: d
Explanation: Gauss law states that the electric flux passing through any closed surface is
equal to the total charge enclosed by the surface. Thus, it is given by, ψ = ∫∫ D.ds= Q,
where the divergence theorem computes the charge and flux, which are both the same.
9. Find the value of divergence theorem for the field D = 2xy i + x2
j for the rectangular
parallelepiped given by x = 0 and 1, y = 0 and 2, z = 0 and 3.

a) 10
b) 12
c) 14
d) 16
View Answer
Answer: b
Explanation: While evaluating surface integral, there has to be two variables and one
constant compulsorily. ∫∫D.ds = ∫∫Dx=0 dy dz + ∫∫Dx=1 dy dz + ∫∫Dy=0 dx dz + ∫∫Dy=2 dx
dz + ∫∫Dz=0 dy dx + ∫∫Dz=3 dy dx. Put D in equation, the integral value we get is 12.
10. If D = 2xy i + 3yz j + 4xz k, how much flux passes through x = 3 plane for which -
1<y<2 and 0<z<4?
a) 12
b) 24
c) 36
d) 48
View Answer
Answer: c
Explanation: By Gauss law, ψ = ∫∫ D.ds, where ds = dydz i at the x-plane. Put x = 3 and
integrate at -1<y<2 and 0<z<4, we get 12 X 3 = 36.
“Volume Integral”.
1. The divergence theorem converts
a) Line to surface integral
b) Surface to volume integral
c) Volume to line integral

d) Surface to line integral
View Answer
Answer: b
Explanation: The divergence theorem is given by, ∫∫ D.ds = ∫∫∫ Div (D) dv. It is clear that
it converts surface (double) integral to volume(triple) integral.
2. The triple integral is used to compute volume. State True/False
a) True
b) False
View Answer
Answer: a
Explanation: The triple integral, as the name suggests integrates the function/quantity
three times. This gives volume which is the product of three independent quantities.
3. The volume integral is three dimensional. State True/False
a) True
b) False
View Answer
Answer: a
Explanation: Volume integral integrates the independent quantities by three times. Thus it
is said to be three dimensional integral or triple integral.
4. Find the charged enclosed by a sphere of charge density ρ and radius a.
a) ρ (4πa2
)
b) ρ(4πa3
/3)
c) ρ(2πa2
)
d) ρ(2πa3
/3)
View Answer
Answer: b
Explanation: The charge enclosed by the sphere is Q = ∫∫∫ ρ dv.

Where, dv = r2
sin θ dr dθ dφ and on integrating with r = 0->a, φ = 0->2π and θ = 0->π,
we get Q = ρ(4πa3
/3).
5. Evaluate Gauss law for D = 5r2
/4 i in spherical coordinates with r = 4m and θ = π/2 as
volume integral.
a) 600
b) 588.9
c) 577.8
d) 599.7
View Answer
Answer: b
Explanation: ∫∫ D.ds = ∫∫∫ Div (D) dv, where RHS needs to be computed.
The divergence of D given is, Div(D) = 5r and dv = r2
sin θ dr dθ dφ. On integrating, r =
0->4, φ = 0->2π and θ = 0->π/4, we get Q = 588.9.
6. Compute divergence theorem for D = 5r2
/4 i in spherical coordinates between r = 1 and
r = 2 in volume integral.
a) 80 π
b) 5 π
c) 75 π
d) 85 π
View Answer
Answer: c
Explanation: D.ds = ∫∫∫ Div (D) dv, where RHS needs to be computed.
The divergence of D given is, Div(D) = 5r and dv = r2
sin θ dr dθ dφ. On integrating, r =
1->2, φ = 0->2π and θ = 0->π, we get Q = 75 π.
7. Compute the Gauss law for D = 10ρ3
/4 i, in cylindrical coordinates with ρ = 4m, z = 0
and z = 5, hence find charge using volume integral.
a) 6100 π

b) 6200 π
c) 6300 π
d) 6400 π
View Answer
Answer: d
Explanation: Q = D.ds = ∫∫∫ Div (D) dv, where RHS needs to be computed.
The divergence of D given is, Div(D) = 10 ρ2
and dv = ρ dρ dφ dz. On integrating, ρ = 0-
>4, φ = 0->2π and z = 0->5, we get Q = 6400 π.
8. Using volume integral, which quantity can be calculated?
a) area of cube
b) area of cuboid
c) volume of cube
d) distance of vector
View Answer
Answer: c
Explanation: The volume integral gives the volume of a vector in a region. Thus volume
of a cube can be computed.
9. Compute the charge enclosed by a cube of 2m each edge centered at the origin and
with the edges parallel to the axes. Given D = 10y3
/3 j.
a) 20
b) 70/3
c) 80/3
d) 30
View Answer
Answer: c
Explanation: Div(D) = 10y2
∫∫∫Div (D) dv = ∫∫∫ 10y2
dx dy dz. On integrating, x = -1->1, y = -1->1 and z = -1->1, we
get Q = 80/3.

10. Find the value of divergence theorem for the field D = 2xy i + x2
j for the rectangular
parallelepiped given by x = 0 and 1, y = 0 and 2, z = 0 and 3.
a) 10
b) 12
c) 14
d) 16
View Answer
Answer: b
Explanation: Div (D) = 2y
∫∫∫Div (D) dv = ∫∫∫ 2y dx dy dz. On integrating, x = 0->1, y = 0->2 and z = 0->3, we get Q
= 12.
“Laplacian Operator”.
1. The point form of Gauss law is given by, Div(V) = ρv
State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: The integral form of Gauss law is ∫∫∫ ρv dv = V. Thus differential or point
form will be Div(V) = ρv.
2. If a function is said to be harmonic, then
a) Curl(Grad V) = 0
b) Div(Curl V) = 0
c) Div(Grad V) = 0
d) Grad(Curl V) = 0
View Answer

Answer: c
Explanation: Though option a & b are also correct, for harmonic fields, the Laplacian of
electric potential is zero. Now, Laplacian refers to Div(Grad V), which is zero for
harmonic fields.
3. The Poisson equation cannot be determined from Laplace equation. State True/False.
a) True
b) False
View Answer
Answer: b
Explanation: The Poisson equation is a general case for Laplace equation. If volume
charge density exists for a field, then (Del)2V= -ρv/ε, which is called Poisson equation.
4. Given the potential V = 25 sin θ, in free space, determine whether V satisfies Laplace’s
equation.
a) Yes
b) No
c) Data sufficient
d) Potential is not defined
View Answer
Answer: a
Explanation: (Del)2
V = 0
(Del)2
V = (Del)2
(25 sin θ), which is not equal to zero. Thus the field does not satisfy
Laplace equation.
5. If a potential V is 2V at x = 1mm and is zero at x=0 and volume charge density is -
106εo, constant throughout the free space region between x = 0 and x = 1mm. Calculate
V at x = 0.5mm.
a) 0.875
b) 0.675

c) 0.475
d) 0.275
View Answer
Answer: d
Explanation: Del2
(V) = -ρv/εo= +106
On integrating twice with respect to x, V = 106. (x2
/2) + C1x + C2.
Substitute the boundary conditions, x = 0, V = 0 and x = 1mm, V = 2V in V,
C1 = 1500 and C2 = 0. At x = 0.5mm, we get, V = 0.875V.
6. Find the Laplace equation value of the following potential field
V = x2
– y2
+ z2
a) 0
b) 2
c) 4
d) 6
View Answer
Answer: b
Explanation: (Del) V = 2x – 2y + 2z
(Del)2 V = 2 – 2 + 2= 2, which is non zero value. Thus it doesn’t satisfy Laplace
equation.
V = ρ cosφ + z
a) 0
b) 1
c) 2
d) 3
View Answer

Answer: a
Explanation: (Del)2
(ρ cosφ + z)= (cos φ/r) – (cos φ/r) + 0
= 0, this satisfies Laplace equation. The value is 0.
V = r cos θ + φ
a) 3
b) 2
c) 1
d) 0
View Answer
Answer: d
Explanation: (Del)2
(r cos θ + φ) = (2 cosθ/r) – (2 cosθ/r) + 0
= 0, this satisfies Laplace equation. This value is 0.
9. The Laplacian operator cannot be used in which one the following?
a) Two dimensional heat equation
b) Two dimensional wave equation
c) Poisson equation
d) Maxwell equation
View Answer
Answer: d
Explanation: The first three options are general cases of Laplacian equation. Maxwell
equation uses only divergence and curl, which is first order differential equation, whereas
Laplacian operator is second order differential equation. Thus Maxwell equation will not
employ Laplacian operator.
10. When a potential satisfies Laplace equation, then it is said to be
a) Solenoidal
b) Divergent

c) Lamellar
d) Harmonic
View Answer
Answer: d
Explanation: A field satisfying the Laplace equation is termed as harmonic field.
“Stoke’s Theorem”.
1. Find the value of Stoke’s theorem for y i + z j + x k.
a) i + j
b) j + k
c) i + j + k
d) –i – j – k
View Answer
Answer: d
Explanation: The curl of y i + z j + x k is i(0-1) – j(1-0) + k(0-1) =
-i –j –k. Since the curl is zero, the value of Stoke’s theorem is zero. The function is said
to be irrotational.
2. The Stoke’s theorem uses which of the following operation?
a) Divergence
b) Gradient
c) Curl
d) Laplacian
View Answer
Answer: c
Explanation: ∫A.dl = ∫∫ Curl (A).ds is the expression for Stoke’s theorem. It is clear that
the theorem uses curl operation.
3. Which of the following theorem convert line integral to surface integral?
a) Gauss divergence and Stoke’s theorem

b) Stoke’s theorem only
c) Green’ s theorem only
d) Stoke’s and Green’s theorem
View Answer
Answer: d
Explanation: The Stoke’s theorem is given by ∫A.dl = ∫∫ Curl (A).ds. Green’s theorem is
given by, ∫ F dx + G dy = ∫∫ (dG/dx – dF/dy) dx dy. It is clear that both the theorems
convert line to surface integral.
4. Find the value of Stoke’s theorem for A = x i + y j + z k. The state of the function will
be
a) Solenoidal
b) Divergent
c) Rotational
d) Curl free
View Answer
Answer: Since curl is required, we need not bother about divergence property. The curl of
the function will be i(0-0) – j(0-0) + k(0-0) = 0. The curl is zero, thus the function is said
to be irrotational or curl free.
5. The Stoke’s theorem can be used to find which of the following?
a) Area enclosed by a function in the given region
b) Volume enclosed by a function in the given region
c) Linear distance
d) Curl of the function
View Answer
Answer: a
Explanation: It states that the line integral of a function gives the surface area of the
function enclosed by the given region. This is computed using the double integral of the
curl of the function.

6. The energy stored in an inductor 2H and current 4A is
a) 4
b) 8
c) 12
d) 16
View Answer
Answer: d
Explanation: From Stoke’s theorem, we can calculate energy stored in an inductor as
0.5Li2
. E = 0.5 X 2 X 42
= 16 units.
7. The voltage of a capacitor 12F with a rating of 2J energy is
a) 0.57
b) 5.7
c) 57
d) 570
View Answer
Answer: a
Explanation: We can compute the energy stored in a capacitor from Stoke’s theorem as
0.5Cv2
. Thus given energy is 0.5 X 12 X v2
. We get v = 0.57 volts.
8. Find the power, given energy E = 2J and current density J = x2
varies from x = 0 and x
= 1.
a) 1/3
b) 2/3
c) 1
d) 4/3
View Answer
Answer: b
Explanation: From Stoke’s theorem, we can calculate P = E X I = ∫ E. J ds
= 2∫ x2
dx as x = 0->1. We get P = 2/3 units.

9. The conductivity of a material with current density 1 unit and electric field 200 μV is
a) 2000
b) 3000
c) 4000
d) 5000
View Answer
Answer: d
Explanation: The current density is given by, J = σE. To find conductivity, σ = J/E =
1/200 X 10-6
= 5000.
10. The resistivity of a material with resistance 200 ohm, length 10m and area twice that
of the length is
a) 200
b) 300
c) 400
d) 500
View Answer
Answer: c
Explanation: Resistance calculated from Ohm’s law and Stoke’s theorem will be R =
ρL/A. To get resistivity, ρ = RA/L = 200 X 20/10 = 400.
“Green’s Theorem”.
1. Mathematically, the functions in Green’s theorem will be
a) Continuous derivatives
b) Discrete derivatives
c) Continuous partial derivatives
d) Discrete partial derivatives
View Answer

Answer: c
Explanation: The Green’s theorem states that if L and M are functions of (x,y) in an open
region containing D and having continuous partial derivatives then,
∫ (F dx + G dy) = ∫∫(dG/dx – dF/dy)dx dy, with path taken anticlockwise.
2. Find the value of Green’s theorem for F = x2
and G = y2
is
a) 0
b) 1
c) 2
d) 3
View Answer
Answer: a
Explanation: ∫∫(dG/dx – dF/dy)dx dy = ∫∫(0 – 0)dx dy = 0. The value of Green’s theorem
gives zero for the functions given.
3. Which of the following is not an application of Green’s theorem?
a) Solving two dimensional flow integrals
b) Area surveying
c) Volume of plane figures
d) Centroid of plane figures
View Answer
Answer: c
Explanation: In physics, Green’s theorem is used to find the two dimensional flow
integrals. In plane geometry, it is used to find the area and centroid of plane figures.
4. The path traversal in calculating the Green’s theorem is
a) Clockwise
b) Anticlockwise
c) Inwards

d) Outwards
View Answer
Answer: b
Explanation: The Green’s theorem calculates the area traversed by the functions in the
region in the anticlockwise direction. This converts the line integral to surface integral.
5. Calculate the Green’s value for the functions F = y2
and G = x2
for the region x = 1 and
y = 2 from origin.
a) 0
b) 2
c) -2
d) 1
View Answer
Answer: c
Explanation: ∫∫(dG/dx – dF/dy)dx dy = ∫∫(2x – 2y)dx dy. On integrating for x = 0->1 and
y = 0->2, we get Green’s value as -2.
6. If two functions A and B are discrete, their Green’s value for a region of circle of
radius a in the positive quadrant is
a) ∞
b) -∞
c) 0
d) Does not exist
View Answer
Answer: d
Explanation: Green’s theorem is valid only for continuous functions. Since the given
functions are discrete, the theorem is invalid or does not exist.
7. Applications of Green’s theorem are meant to be in
a) One dimensional

b) Two dimensional
c) Three dimensional
d) Four dimensional
View Answer
Answer: b
Explanation: Since Green’s theorem converts line integral to surface integral, we get the
value as two dimensional. In other words the functions are variable with respect to x,y,
which is two dimensional.
8. The Green’s theorem can be related to which of the following theorems
mathematically?
a) Gauss divergence theorem
b) Stoke’s theorem
c) Euler’s theorem
d) Leibnitz’s theorem
View Answer
Answer: b
Explanation: The Green’s theorem is a special case of the Kelvin- Stokes theorem, when
applied to a region in the x-y plane. It is a widely used theorem in mathematics and
physics.
9. The Shoelace formula is a shortcut for the Green’s theorem. State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: The Shoelace theorem is used to find the area of polygon using cross
multiples. This can be verified by dividing the polygon into triangles. It is a special case
of Green’s theorem.

10. Find the area of a right angled triangle with sides of 90 degree unit and the functions
described by L = cos y and M = sin x.
a) 0
b) 45
c) 90
d) 180
View Answer
Answer: d
Explanation: dM/dx = cos x and dL/dy = -sin y
∫∫(dM/dx – dL/dy)dx dy = ∫∫ (cos x + sin y)dx dy. On integrating with x = 0->90 and y =
0->90, we get area of right angled triangle as -180 units (taken in clockwise direction).
Since area cannot be negative, we take 180 units
“Gauss Divergence Theorem”.
1. Gauss theorem uses which of the following operations?
a) Gradient
b) Curl
c) Divergence
d) Laplacian
View Answer
Answer: c
Explanation: The Gauss divergence theorem uses divergence operator to convert surface
to volume integral. It is used to calculate the volume of the function enclosing the region
given.
2. Evaluate the surface integral ∫∫ (3x i + 2y j). dS, where S is the sphere given by x2
+
y2
+ z2
= 9.
a) 120π
b) 180π

c) 240π
d) 300π
View Answer
Answer: b
Explanation: We could parameterise surface and find surface integral, but it is wise to use
divergence theorem to get faster results. The divergence theorem is given by ∫∫ F.dS = ∫∫∫
Div (F).dV
Div (3x i + 2y j) = 3 + 2 = 5. Now the volume integral will be ∫∫∫ 5.dV, where dV is the
volume of the sphere 4πr3
/3 and r = 3units.Thus we get 180π.
3. The Gauss divergence theorem converts
a) line to surface integral
b) line to volume integral
c) surface to line integral
d) surface to volume integral
View Answer
Answer: d
Explanation: The divergence theorem for a function F is given by ∫∫ F.dS = ∫∫∫ Div (F).dV.
Thus it converts surface to volume integral.
4. The divergence theorem for a surface consisting of a sphere is computed in which
coordinate system?
a) Cartesian
b) Cylindrical
c) Spherical
d) Depends on the function
View Answer
Answer: d
Explanation: Seeing the surface as sphere, we would immediately choose spherical

system, but it is wrong. The divergence operation is performed in that coordinate system
in which the function belongs to. It is independent of the surface region.
5. Find the Gauss value for a position vector in Cartesian system from the origin to one
unit in three dimensions.
a) 0
b) 3
c) -3
d) 1
View Answer
Answer: b
Explanation: The position vector in Cartesian system is given by R = x i + y j + z k.
Div(R) = 1 + 1 + 1 = 3. By divergence theorem, ∫∫∫3.dV, where V is a cube with x = 0->1,
y = 0->1 and z = 0->1. On integrating, we get 3 units.
6. The divergence theorem value for the function x2
+ y2
+ z2
at a distance of one unit
from the origin is
a) 0
b) 1
c) 2
d) 3
View Answer
Answer: d
Explanation: Div (F) = 2x + 2y + 2z. The triple integral of the divergence of the function
is ∫∫∫(2x + 2y + 2z)dx dy dz, where x = 0->1, y = 0->1 and z = 0->1. On integrating, we
get 3 units.
7. If a function is described by F = (3x + z, y2
− sin x2
z, xz + yex5
), then the divergence
theorem value in the region 0<x<1, 0<y<3 and 0<z<2 will be
a) 13

b) 26
c) 39
d) 51
View Answer
Answer: c
Explanation: Div (F) = 3 + 2y + x. By divergence theorem, the triple integral of Div F in
the region is ∫∫∫ (3 + 2y + x) dx dy dz. On integrating from x = 0->1, y = 0->3 and z = 0-
>2, we get 39 units.
8. Find the divergence theorem value for the function given by (ez
, sin x, y2
)
a) 1
b) 0
c) -1
d) 2
View Answer
Answer: b
Explanation: Since the divergence of the function is zero, the triple integral leads to zero.
The Gauss theorem gives zero value.
9. For a function given by F = 4x i + 7y j +z k, the divergence theorem evaluates to which
of the values given, if the surface considered is a cone of radius 1/2π m and height 4π2
m.
a) 1
b) 2
c) 3
d) 4
View Answer
Answer: b
Explanation: Div (F) = 4 + 7 + 1 = 12. The divergence theorem gives ∫∫∫(12).dV, where
dV is the volume of the cone πr3
h/3, where r = 1/2π m and h = 4π2
m. On substituting the
radius and height in the triple integral, we get 2 units.

10. Divergence theorem computes to zero for a solenoidal function. State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: The divergence theorem is given by, ∫∫ F.dS = ∫∫∫ Div (F).dV, for a function
F. If the function is solenoidal, its divergence will be zero. Thus the theorem computes to
zero.
“Coulomb law”.
1. Coulomb is the unit of which quantity?
a) Field strength
b) Charge
c) Permittivity
d) Force
View Answer
Answer: b
Explanation: The standard unit of charge is Coulomb. One coulomb is defined as the 1
Newton of force applied on 1 unit of electric field.
2. Coulomb law is employed in
a) Electrostatics
b) Magnetostatics
c) Electromagnetics
d) Maxwell theory
View Answer
Answer: a
Explanation: Coulomb law is applied to static charges. It states that force between any

two point charges is proportional to the product of the charges and inversely proportional
to square of the distance between them. Thus it is employed in electrostatics.
3. Find the force between 2C and -1C separated by a distance 1m in air(in newton).
a) 18 X 106
b) -18 X 106
c) 18 X 10-6
d) -18 X 10-6
View Answer
Answer: b
Explanation: F = q1q2/(4∏εor2
) = -2 X 9/(10-9
X 12) = -18 X 109
.
4. Two charges 1C and -4C exists in air. What is the direction of force?
a) Away from 1C
b) Away from -4C
c) From 1C to -4C
d) From -4C to 1C
View Answer
Answer: c
Explanation: Since the charges are unlike, the force will be attractive. Thus the force
directs from 1C to -4C.
5. Find the force of interaction between 60 stat coulomb and 37.5 stat coulomb spaced
7.5cm apart in transformer oil(εr=2.2) in 10-4
N,
a) 8.15
b) 5.18
c) 1.518
d) 1.815
View Answer

Answer: d
Explanation: 1 stat coulomb = 1/(3 X 109
) C
F = (1.998 X 1.2488 X 10-16
)/(4∏ X 8.854 X 10-12
X 2.2 X (7.5 X 10-2
)2
) = 1.815 X 10-4
N.
6. Find the force between two charges when they are brought in contact and separated by
4cm apart, charges are 2nC and -1nC, in μN.
a) 1.44
b) 2.44
c) 1.404
d) 2.404
View Answer
Answer: c
Explanation: Before the charges are brought into contact, F = 11.234 μN.
After charges are brought into contact and then separated, charge on each sphere is, (q1 +
q2)/2 = 0.5nC
On calculating the force with q1 = q2 = 0.5nC, F = 1.404μN.
7. The Coulomb law is an implication of which law?
a) Ampere law
b) Gauss law
c) Biot Savart law
d) Lenz law
View Answer
Answer: b
Explanation: The Coulomb law can be formulated from the Gauss law, using the
divergence theorem. Thus it is an implication of Gauss law.
8. Two small diameter 10gm dielectric balls can slide freely on a vertical channel. Each
carry a negative charge of 1μC. Find the separation between the balls if the lower ball is
restrained from moving.

a) 0.5
b) 0.4
c) 0.3
d) 0.2
View Answer
Answer: c
Explanation: F = mg = 10 X 10-3
X 9.81 = 9.81 X 10-2
N.
On calculating r by substituting charges, we get r = 0.3m.
9. A charge of 2 X 10-7
C is acted upon by a force of 0.1N. Determine the distance to the
other charge of 4.5 X 10-7
C, both the charges are in vacuum.
a) 0.03
b) 0.05
c) 0.07
d) 0.09
View Answer
Answer: d
Explanation: F = q1q2/(4∏εor2
) , substituting q1, q2 and F, r2 = q1q2/(4∏εoF) =
We get r = 0.09m.
10. For a charge Q1, the effect of charge Q2 on Q1 will be,
a) F1 = F2
b) F1 = -F2
c) F1 = F2 = 0
d) F1 and F2 are not equal
View Answer
Answer: b
Explanation: The force of two charges with respect with each other is given by F1 and
F2. Thus F1 + F2 = 0 and F1 = -F2.

“Electric Field Intensity”.
1. The electric field intensity is defined as
a) Force per unit charge
b) Force on a test charge
c) Force per unit charge on a test charge
d) Product of force and charge
View Answer
Answer: c
Explanation: The electric field intensity is the force per unit charge on a test charge, i.e,
q1 = 1C. E = F/Q = Q/(4∏εr2).
2. Find the force on a charge 2C in a field 1V/m.
a) 0
b) 1
c) 2
d) 3
View Answer
Answer: c
Explanation: Force is the product of charge and electric field.
F = q X E = 2 X 1 = 2 N.
3. Find the electric field intensity of two charges 2C and -1C separated by a distance 1m
in air.
a) 18 X 109
b) 9 X 109
c) 36 X 109
d) -18 X 109
View Answer

Answer: b
Explanation: F = q1q2/(4∏εor2) = -2 X 9/(10-9
X 12) = -18 X 109
E = F/q = 18 X 109
/2 = 9 X 109
.
4. What is the electric field intensity at a distance of 20cm from a charge 2 X 10-6
C in
vacuum?
a) 250,000
b) 350,000
c) 450,000
d) 550,000
View Answer
Answer: c
Explanation: E = Q/ (4∏εor2)
= (2 X 10-6
)/(4∏ X εo X 0.22
) = 450,000 V/m.
5. Determine the charge that produces an electric field strength of 40 V/cm at a distance
of 30cm in vacuum(in 10-8
C)
a) 4
b) 2
c) 8
d) 6
View Answer
Answer: a
Explanation: E = Q/ (4∏εor2
)
Q = (4000 X 0.32
)/ (9 X 109
) = 4 X 10-8
C.
6. The field intensity of a charge defines the impact of the charge on a test charge placed
at a distance. It is maximum at d = 0cm and minimises as d increases. State True/False
a) True

b) False
View Answer
Answer: a
Explanation: If a test charge +q is situated at a distance r from Q, the test charge will
experience a repulsive force directed radially outward from Q. Since electric field is
inversely proportional to distance, thus the statement is true.
7. Electric field of an infinitely long conductor of charge density λ, is given by E =
λ/(2πεh).aN. State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: The electric field intensity of an infinitely long conductor is given by, E =
λ/(4πεh).(sin α2 – sin α1)i + (cos α2 + cos α1)j
For an infinitely long conductor, α = 0. E = λ/(4πεh).(cos 0 + cos 0) = λ/(2πεh).aN.
8. Electric field intensity due to infinite sheet of charge σ is
a) Zero
b) Unity
c) σ/ε
d) σ/2ε
View Answer
Answer: d
Explanation: E = σ/2ε.(1- cos α), where α = h/(√(h2
+a2
))
Here, h is the distance of the sheet from point P and a is the radius of the sheet. For
infinite sheet, α = 90. Thus E = σ/2ε.
9. For a test charge placed at infinity, the electric field will be
a) Unity

b) +∞
c) Zero
d) -∞
View Answer
Answer: c
Explanation: E = Q/ (4∏εor2
)
When distance d is infinity, the electric field will be zero, E= 0.
10. In electromagnetic waves, the electric field will be perpendicular to which of the
following?
a) Magnetic field intensity
b) Wave propagation
c) Both H and wave direction
d) It propagates independently
View Answer
Answer: c
Explanation: In an electromagnetic wave, the electric field and magnetic field will be
perpendicular to each other. Both of these fields will be perpendicular to the wave
propagation
“Electric Field Density”.
1. The lines of force are said to be
a) Real
b) Imaginary
c) Drawn to trace the direction
d) Not significant
View Answer
Answer: c
Explanation: The lines drawn to trace the direction in which a positive test charge will

experience force due to the main charge are called lines of force. They are not real but
drawn for our interpretation.
2. Electric flux density in electric field is referred to as
a) Number of flux lines
b) Ratio of flux lines crossing a surface and the surface area
c) Direction of flux at a point
d) Flux lines per unit area
View Answer
Answer: b
Explanation: Electric flux density is given by the ratio between number of flux lines
crossing a surface normal to the lines and the surface area. The direction of D at a point is
the direction of the flux lines at that point.
3. The electric flux density is the
a) Product of permittivity and electric field intensity
b) Product of number of flux lines and permittivity
c) Product of permeability and electric field intensity
d) Product of number of flux lines and permeability
View Answer
Answer: a
Explanation: D= εE, where ε=εoεr is the permittivity of electric field and E is the electric
field intensity. Thus electric flux density is the product of permittivity and electric field
intensity.
4. Which of the following correctly states Gauss law?
a) Electric flux is equal to charge
b) Electric flux per unit volume is equal to charge
c) Electric field is equal to charge density

d) Electric flux per unit volume is equal to volume charge density
View Answer
Answer: d
Explanation: The electric flux passing through any closed surface is equal to the total
charge enclosed by that surface. In other words, electric flux per unit volume leaving a
point (vanishing small volume), is equal to the volume charge density.
5. The Gaussian surface is
a) Real boundary
b) Imaginary surface
c) Tangential
d) Normal
View Answer
Answer: b
Explanation: It is any physical or imaginary closed surface around a charge which
satisfies the following condition: D is everywhere either normal or tangential to the
surface so that D.ds becomes either Dds or 0 respectively.
6. Find the flux density of a sheet of charge density 25 units in air.
a) 25
b) 12.5
c) 6.25
d) 3.125
View Answer
Answer: b
Explanation: Electric field intensity of infinite sheet of charge E = σ/2ε.
Thus D = εE = σ/2 = 25/2 = 12.5.
7. A uniform surface charge of σ = 2 μC/m2
, is situated at z = 2 plane. What is the value
of flux density at P(1,1,1)m?

a) 10-6
b) -10-6
c) 106
d) -106
View Answer
Answer: b
Explanation: The flux density of any field is independent of the position (point). D = σ/2
= 2 X 10-6
(-az)/2 = -10-6
.
8. Find the flux density of line charge of radius (cylinder is the Gaussian surface) 2m and
charge density is 3.14 units?
a) 1
b) 0.75
c) 0.5
d) 0.25
View Answer
Answer: d
Explanation: The electric field of a line charge is given by, E = λ/(2περ), where ρ is the
radius of cylinder, which is the Gaussian surface and λ is the charge density. The density
D = εE = λ/(2πρ) = 3.14/(2π X 2) = 1/4 = 0.25.
9. If the radius of a sphere is 1/(4π)m and the electric flux density is 16π units, the total
flux is given by,
a) 2
b) 3
c) 4
d) 5
View Answer

Answer: c
Explanation: Total flux leaving the entire surface is, ψ = 4πr2
D from Gauss law. Ψ =
4π(1/16π2
) X 16π = 4.
10. Find the electric field intensity of transformer oil (εr = 2 approx) with density 1/4π (in
109
units)
a) 2.5
b) 3.5
c) 4.5
d) 5.5
View Answer
Answer: c
Explanation: D = εE. E = (1/4π)/(2Xεo) = 4.5 X 109
units.
“Electric Potential”.
1. Potential difference is the work done in moving a unit positive charge from one point
to another in an electric field. State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: The electric potential is the ratio of work done to the charge. Also it is the
work done in moving a unit positive charge from infinity to a point in an electric field.
2. A point charge 2nC is located at origin. What is the potential at (1,0,0)?
a) 12
b) 14
c) 16
d) 18
View Answer

Answer: d
Explanation: V = Q/(4πεr), where r = 1m
V = (2 X 10-9
)/(4πε x 1) = 18 volts.
3. Six equal point charges Q = 10nC are located at 2,3,4,5,6,7m. Find the potential at
origin.
a) 140.35
b) 141.35
c) 142.35
d) 143.35
View Answer
Answer: d
Explanation: V = (1/4πεo) ∑Q/r = (10 X 10-9
/4πεo)
(0.5 + 0.33 + 0.25 + 0.2 + 0.166 + 0.142) = 143.35 volts.
4. A point charge 0.4nC is located at (2, 3, 3). Find the potential differences between (2,
3, 3)m and (-2, 3, 3)m due to the charge.
a) 2.5
b) 2.6
c) 2.7
d) 2.8
View Answer
Answer: c
Explanation: Vab = (Q/4πεo)(1/rA) + (1/rB), where rA and rB are position vectors rA =
1m and rB = 4m. Thus Vab = 2.7 volts.
5. Find the potential of V = 60sin θ/r2
at P(3,60,25)
a) 5.774
b) 6.774
c) 7.774

d) 8.774
View Answer
Answer: a
Explanation: V = 60sin θ/r2
, put r = 3m, θ = 60 and φ = 25, V = 60 sin 60/32
= 5.774 volts.
6. Given E = 40xyi + 20x2
j + 2k. Calculate the potential between two points (1,-1,0) and
(2,1,3).
a) 105
b) 106
c) 107
d) 108
View Answer
Answer: b
Explanation: V = -∫ E.dl = -∫ (40xy dx + 20x2
dy + 2 dz), from (2,1,3) to (1,-1,0), we get
Vpq on integrating from Q to P. Vpq = 106 volts.
7. The potential difference in an open circuit is
a) Zero
b) Unity
c) Infinity
d) Circuit does not exist open
View Answer
Answer: c
Explanation: In an open circuit no current exists due to non-existence of loops. Also
voltage/potential will be infinity in an open circuit.
8. The potential taken between two points across a resistor will be
a) Positive
b) Negative
c) Zero

d) Infinity
View Answer
Answer: b
Explanation: The resistor will absorb power and dissipate it in the form of heat energy.
The potential between two points across a resistor will be negative.
9. What is the potential difference between 10sinθcosφ/r2
at A(1,30,20) and B(4,90,60)?
a) 2.386
b) 3.386
c) 4.386
d) 5.386
View Answer
Answer: c
Explanation: Potential at A, Va = 10sin30cos20/12
= 4.6985 and Potential at B, Vb =
10sin90cos60/42
= 0.3125. Potential difference between A and B is, Vab = 4.6985 –
0.3125 = 4.386 volts.
10. The voltage at any point in an ac circuit will be
a) Peak voltage
b) RMS voltage
c) Average voltage
d) Source voltage
View Answer
Answer: b
Explanation: In any ac circuit, the voltage measured will not be exact maximum. In order
to normalise, we assume the instantaneous voltage at any point be 70.7% of the peak
value, which is called the root mean square (RMS)voltage
“Gauss Law”.

1. Divergence theorem is based on
a) Gauss law
b) Stoke’s law
c) Ampere law
d) Lenz law
View Answer
Answer: a
Explanation: The divergence theorem relates surface integral and volume integral.
Div(D) = ρv, which is Gauss’s law.
2. The Gaussian surface for a line charge will be
a) Sphere
b) Cylinder
c) Cube
d) Cuboid
View Answer
Answer: b
Explanation: A line charge can be visualized as a rod of electric charges. The three
dimensional imaginary enclosed surface of a rod can be a cylinder.
3. The Gaussian surface for a point charge will be
a) Cube
b) Cylinder
c) Sphere
d) Cuboid
View Answer
Answer: c
Explanation: A point charge is single dimensional. The three dimensional imaginary
enclosed surface of a point charge will be sphere.

4. A circular disc of radius 5m with a surface charge density ρs = 10sinφ is enclosed by
surface. What is the net flux crossing the surface?
a) 3
b) 2
c) 1
d) 0
View Answer
Answer: d
Explanation: Q = ∫ ρsds = ∫∫ 10sinφ rdrdφ, on integrating with r = 0->5 and φ = 0->2π, we
get Q = ψ = 0.
5. The total charge of a surface with densities 1,2,…,10 is
a) 11
b) 33
c) 55
d) 77
View Answer
Answer: c
Explanation: Q = ∫∫D.ds. Since the data is discrete, the total charge will be summation of
1,2,…,10,i.e, 1+2+…+10 = 10(11)/2 = 55.
6. The work done by a charge of 10μC with a potential 4.386 is (in μJ)
a) 32.86
b) 43.86
c) 54.68
d) 65.68
View Answer
Answer: b
Explanation: By Gauss law principles, W = Q X V = 10 X 10-6
X 4.386 = 43.86 X 10-
6
joule.

7. The potential of a coaxial cylinder with charge density 1 unit , inner radius 1m and
outer cylinder 2m is (in 109
)
a) 12.74
b) 13.47
c) 12.47
d) 13.74
View Answer
Answer: c
Explanation: The potential of a coaxial cylinder will be ρl ln(b/a)/2πε, where ρl = 1, b =
2m and a = 1m. We get V = 12.47 X 109
volts.
8. Find the potential due to a charged ring of density 2 units with radius 2m and the point
at which potential is measured is at a distance of 1m from the ring.
a) 18π
b) 24π
c) 36π
d) 72π
View Answer
Answer: d
Explanation: The potential due to a charged ring is given by λa/2εr, where a = 2m and r =
1m. We get V = 72π volts.
9. Gauss law cannot be used to find which of the following quantity?
a) Electric field intensity
b) Electric flux density
c) Charge
d) Permittivity
View Answer
Answer: d
Explanation: Permittivity is constant for a particular material(say permittivity of water is

1). It cannot be determined from Gauss law, whereas the remaining options can be
computed from Gauss law.
10. Gauss law for magnetic fields is given by
a) Div(E) = 0
b) Div(B) = 0
c) Div(H) = 0
d) Div(D) = 0
View Answer
Answer: b
Explanation: The divergence of magnetic flux density is always zero. This is called Gauss
law for magnetic fields. It implies the non-existence of magnetic monopoles in any
magnetic field.
“Applications of Gauss Law”.
1. Gauss law can be used to compute which of the following?
a) Permittivity
b) Permeability
c) Radius of Gaussian surface
d) Electric potential
View Answer
Answer: c
Explanation: Gauss law relates the electric flux density and the charge density. Thus it
can be used to compute radius of the Gaussian surface. Permittivity and permeability are
constants for a particular material.
2. Three charged cylindrical sheets are present in three spaces with σ = 5 at R = 2m, σ = -
2 at R = 4m and σ = -3 at R = 5m. Find the flux density at R = 1m.

a) 0
b) 1
c) 2
d) 3
View Answer
Answer: a
Explanation: Since 1m does not enclose any cylinder (three Gaussian surfaces of radius
2m, 4m, 5m exists), the charge density and charge becomes zero according to Gauss law.
Thus flux density is also zero.
a) 3
b) 10/3
c) 11/3
d) 4
View Answer
Answer: b
Explanation: The radius is 3m, hence it will enclose one Gaussian cylinder of R = 2m.
By Gauss law, ψ = Q
D(2πRL) = σ(2πRL), D(2π X 3) = σ(2π X 2), Thus D = 10/3 units.
2 at R = 4m and σ =-3 at R = 5m. Find the flux density at R = 4.5m.
a) 4/4.5
b) 3/4.5
c) 2/4.5
d) 1/4.5
View Answer

Answer: c
Explanation: The Gaussian cylinder of R = 4.5m encloses sum of charges of two
cylinders (R = 2m and R = 4m).
D(2πRL) = σ(2πRL), D(2π X 4.5) = Q1 + Q2 = σ1(2π X 2) + σ2(2π X 4), here σ1 = 5 and
σ2 = -2. We get D = 2/4.5 units.
a) 17/6
b) -17/6
c) 13/6
d) -13/6
View Answer
Answer: d
Explanation: The radius R = 6m encloses all the three Gaussian cylinders.
D(2πRL) = σ(2πRL), D(2π X 6) = Q1 + Q2 + Q3 = σ1(2π X 2) + σ2(2π X 4) + σ3(2π X
5), here σ1 = 5, σ2 = -2 and σ3 = -3. We get D = -13/6 units.
6. Gauss law can be evaluated in which coordinate system?
a) Cartesian
b) Cylinder
c) Spherical
d) Depends on the Gaussian surface
View Answer
Answer: d
Explanation: The Gauss law exists for all materials. Depending on the Gaussian surface
of the material, we take the coordinate systems accordingly. Suppose if the material is a

coaxial cable, the Gaussian surface is in the form of cylinder. Thus we take
Cylinder/Circular coordinate system.
7. Gauss law cannot be expressed in which of the following forms?
a) Differential
b) Integral
c) Point
d) Stokes theorem
View Answer
Answer: d
Explanation: Gauss law can be expressed in differential or point form as,
Div (D)= ρv and in integral form as ∫∫ D.ds = Q = ψ . It is not possible to express it using
Stoke’s theorem.
8. The tangential component of electric field intensity is always continuous at the
interface. State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: Consider a dielectric-dielectric boundary, the electric field intensity in both
the surfaces will be Et1 = Et2, which implies that the tangential component of electric
field intensity is always continuous at the boundary.
9. The normal component of the electric flux density is always discontinuous at the
interface. State True/False.
a) True
b) False
View Answer

Answer: a
Explanation: In a dielectric-dielectric boundary, if a free surface charge density exists at
the interface, then the normal components of the electric flux density are discontinuous at
the boundary, which means Dn1 = Dn2.
10. With Gauss law as reference which of the following law can be derived?
a) Ampere law
b) Faraday’s law
c) Coulomb’s law
d) Ohm’s law
View Answer
Answer: c
Explanation: From Gauss law, we can compute the electric flux density. This in turn can
be used to find electric field intensity. We know that F = qE. Hence force can be
computed. This gives the Coulomb’s law.
“Relation of E,D,V”.
1. The electric flux density and electric field intensity have which of the following
relation?
a) Linear
b) Nonlinear
c) Inversely linear
d) Inversely nonlinear
View Answer
Answer: a
Explanation: The electric flux density is directly proportional to electric field intensity.
The proportionality constant is permittivity. D=ε E. It is clear that both are in linear
relationship.

2. The electric field intensity is the negative gradient of the electric potential. State
True/False.
a) True
b) False
View Answer
Answer: a
Explanation: V = -∫E.dl is the integral form. On differentiating both sides, we get E = -
Grad (V). Thus the electric field intensity is the negative gradient of the electric potential.
3. Find the electric potential for an electric field 3units at a distance of 2m.
a) 9
b) 4
c) 6
d) 3/2
View Answer
Answer: c
Explanation: The electric field intensity is the ratio of electric potential to the distance. E
= V/d. To get V = E X d = 3 X 2 = 6units.
4. Find the potential at a point (4, 3, -6) for the function V = 2x2
y + 5z.
a) 96
b) 66
c) 30
d) -66
View Answer
Answer: b
Explanation: The electric potential for the function V = 2x2
y + 5z at the point (4, 3, -6) is
given by V = 2(4)2(3) + 5(-6) = 96-30 = 66 units.

5. Find the electric flux density surrounding a material with field intensity of 2xyz placed
in transformer oil ( εr = 2.2) at the point P(1,2,3) is
(in 10-10
units)
a) 2.1
b) 2.33
c) 2.5
d) 2.77
View Answer
Answer: c
Explanation: D = εE, where ε = εo εr. The flux density is given by,
D = 8.854 X 10-12
X 2.2 X 2(1)(2)(3) = 2.33 X 10-10
units.
6. If potential V = 20/(x2
+ y2
). The electric field intensity for V is
40(x i + y j)/(x2
+ y2
)2
. State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: E = -Grad (V) = -Grad(20/(x2
+ y2
)) = -(-40x i /(x2
+ y2
)2
– 40(y j)/(x2
+ y2
)2
)
= 40(x i + y j)/(x2
+ y2
)2
. Thus the statement is true.
7. Find the potential of the function V = 60cos θ/r at the point P(3, 60, 25).
a) 20
b) 10
c) 30
d) 60
View Answer
Answer: b
Explanation: Given V = 60cos θ/r. For r = 3m and θ = 60, we get V = 60cos 60/3 = 20cos
60 = 10 units.

8. Find the work done moving a charge 2C having potential V = 24volts is
a) 96
b) 24
c) 36
d) 48
View Answer
Answer: d
Explanation: The work done is the product of charge and potential.
W = Q X V = 2 X 24 = 48 units.
9. If the potential is given by, V = 10sin θ cosφ/r, find the density at the point P(2, π/2, 0)
(in 10-12
units)
a) 13.25
b) 22.13
c) 26.31
d) 31.52
View Answer
Answer: b
Explanation: Since V is given find out E.E = -Grad(V) = – Grad(10sin θ cosφ/r). From E,
we can easily compute D. D = εE = 8.854 X 10-12
X 5/2 = 22.13 units.
10. If V = 2x2
y + 20z – 4/(x2
+ y2
), find the density at A(6, -2.5, 3) in nC/m2
.
a) 0.531i – 0.6373j – 0.177k
b) 0.6373i – 0.177j -0.531k
c) 0.177i – 0.6373j – 0.531k
d) 0.531i – 0.177j – 0.6373k
View Answer
Answer: a
Explanation: Find E from V, E = -Grad (V). We get E at A(6,-2.5,3) as 59.97i – 71.98j -

20k. Thus D = εE = 8.854 X 10-12
X
(59.97i – 71.98j -20k) = (0.531i – 0.6373j – 0.177k) nC/m2
.
“Real Time Applications”.
1. Calculate the capacitance of a material in air with area 20 units and distance between
plates is 5m.
a) 35.36pF
b) 3.536pF
c) 35.36nF
d) 3.536nF
View Answer
Answer: a
Explanation: The capacitance of any material is given by, C = εA/d, where ε = εoεr is the
permittivity in air and the material respectively. Thus C = 1 X 8.854 X 10-12
X 20/5 =
35.36pF.
2. The resistance of a material with conductivity 2millimho/m2
, length 10m and area 50m
is
a) 500
b) 200
c) 100
d) 1000
View Answer
3. Find the inductance of a coil with permeability 3.5, turns 100 and length 2m. Assume
the area to be thrice the length.
a) 131.94mH
b) 94.131mH
c) 131.94H

d) 94.131H
View Answer
Answer: a
Explanation: The inductance is given by L = μ N2
A/l, where μ= μoμr is the permeability
of air and the material respectively. N = 100 and Area = 3 X 2 = 6. L = 4π X 10-7
X
1002
X 6/2 = 131.94mH.
4. Find the current density of a material with resistivity 20 units and electric field
intensity 2000 units.
a) 400
b) 300
c) 200
d) 100
View Answer
Answer: d
Explanation: The current density is given by J = σ E, where σ is the conductivity. Thus
resistivity ρ = 1/σ. J = E/ρ = 2000/20 = 100 units.
5. Find the current in a conductor with resistance 2 ohm, electric field 2 units and
distance 100cm.
a) 1A
b) 10mA
c) 10A
d) 100mA
View Answer
Answer: a
Explanation: We know that E = V/d. To get potential, V = E X d = 2 X 1 = 2 volts. From
Ohm’s law, V = IR and current I = V/R = 2/2 = 1A.

6. In electric fields, D= ε E. The correct expression which is analogous in magnetic fields
will be
a) H = μ B
b) B = μ H
c) A = μ B
d) H = μ A
View Answer
Answer: b
Explanation: In electric fields, the flux density is a product of permittivity and field
intensity. Similarly, for magnetic fields, the magnetic flux density is the product of
permeability and magnetic field intensity, given by B= μ H.
7. Find the force on a conductor of length 12m and magnetic flux density 20 units when a
current of 0.5A is flowing through it.
a) 60
b) 120
c) 180
d) 200
View Answer
Answer: b
Explanation: The force on a conductor is given by F = BIL, where B = 20, I = 0.5 and L =
12. Force F = 20 X 0.5 x 12 = 120 N.
8. From the formula F = qE, can prove that work done is a product of force and
displacement. State True/False
a) True
b) False
View Answer

Answer: a
Explanation: We know that F = qE = qV/d and W = qV. Thus it is clear that qV = W and
qV = Fd. On equating both, we get W = Fd, which is the required proof.
9. Calculate the power of a material with electric field 100 units at a distance of 10cm
with a current of 2A flowing through it.
a) 10
b) 20
c) 40
d) 80
View Answer
Answer: b
Explanation: Power is defined as the product of voltage and current.
P = V X I, where V = E X d. Thus P = E X d X I = 100 X 0.1 X 2 = 20 units.
10. Compute the power consumed by a material with current density 15 units in an area
of 100 units. The potential measured across the material is 20V.
a) 100kJ
b) 250kJ
c) 30kJ
d) 15kJ
View Answer
Answer: c
Explanation: Power is given by, P= V X I, where I = J X A is the current.
Thus power P = V X J X A = 20 X 15 X 100 = 30,000 joule = 30kJ.
“Electric Dipole”.
1. Choose the best definition of a dipole.
a) A pair of equal and like charges located at the origin
b) A pair of unequal and like charges located at the origin

c) A pair of equal and unlike charges separated by a small distance
d) A pair of unequal and unlike charges separated by a small distance
View Answer
Answer: c
Explanation: An electric dipole generally refers to two equal and unlike (opposite signs)
charges separated by a small distance. It can be anywhere, not necessarily at origin.
2. The potential due to a dipole at a point P from it is the
a) Sum of potentials at the charges
b) Difference of potentials at the charges
c) Multiplication of potentials at the charges
d) Ratio of potentials at the charges
View Answer
Answer: b
Explanation: The total potential at the point P due to the dipole is given by the difference
of the potentials of the individual charges.
V = V1 + (-V2), since both the charges are unlike. Thus V = V1 – V2.
3. Calculate the dipole moment of a dipole with equal charges 2C and -2C separated by a
distance of 2cm.
a) 0.02
b) 0.04
c) 0.06
d) 0.08
View Answer
Answer: b
Explanation: The dipole moment of charge 2C and distance 2cm will be,
M = Q x d. Thus, M = 2 x 0.02 = 0.04 C-m.

4. Find the angle at which the potential due a dipole is measured, when the distance from
one charge is 12cm and that due to other is 11cm, separated to each other by a distance of
2cm.
a) 15
b) 30
c) 45
d) 60
View Answer
Answer: d
Explanation: Here, the two charges are separated by d = 2cm.
The distance from one charge (say Q1) will be R1 = 11cm. The distance from another
charge (say Q2) will be R2 = 12cm. If R1 and R2 is assumed to be parallel, then R2 – R1
= d cos θ. We get 1 = 2cos θ and cos θ = 0.5. Then θ =
cos-1
(0.5) = 60.
5. Find the potential due the dipole when the angle subtended by the two charges at the
point P is perpendicular.
a) 0
b) Unity
c) ∞
d) -∞
View Answer
Answer: a
Explanation: The potential due the dipole is given by, V = m cos θ/(4πεr2
). When the
angle becomes perpendicular (θ = 90). The potential becomes zero since cos 90 will
become zero.
6. For two charges 3C and -3C separated by 1cm and are located at distances 5cm and
7cm respectively from the point P, then the distance between their midpoint and the point
P will be

a) 5.91
b) 12.6
c) 2
d) 9
View Answer
Answer: a
Explanation: For a distant point P, the R1 and R2 will approximately be equal.
R1 = R2 = r, where r is the distance between P and the midpoint of the two charges. Thus
they are in geometric progression, R1R2=r2
Now, r2 = 5 x 7 = 35. We get r = 5.91cm.
7. Calculate the distance between two charges of 4C forming a dipole, with a dipole
moment of 6 units.
a) 1
b) 1.5
c) 2
d) 2.5
View Answer
Answer: b
Explanation: The dipole moment is given by, M = Q x d. To get d, we rearrange the
formula d = M/Q = 6/4 = 1.5units.
8. The potential due to the dipole on the midpoint of the two charges will be
a) 0
b) Unity
c) ∞
d) -∞
View Answer
9. Dipoles in any electric field undergo
a) Magnetism

b) Electromagnetism
c) Magnetisation
d) Polarisation
View Answer
Answer: d
Explanation: Dipoles in any pure electric field will undergo polarisation. It is the process
of alignment of dipole moments in accordance with the electric field applied.
10. Dipole moments are used to calculate the
a) Electric field intensity
b) Polarisation patterns
c) Strength of the dipole in the field
d) Susceptibility
View Answer
Answer: b
Explanation: Dipole moment implicates the strength of the dipole in the electric field.
They are then used to compute the polarisation patterns based on the applied field. Once
the polarisation is determined we can find its susceptibility. Though all options seem to
be correct, the apt answer is to calculate polarisation, provided applied field is known.
“Electrostatic Energy”.
1. The electrostatic energy in an electric field does not depend on which of the following?
a) Magnitude of charges
b) Permittivity
c) Applied electric field
d) Flux lines
View Answer
Answer: c
Explanation: The energy in an electric field directly magnitude of charges. Thus electric

field and flux density are also dependent. But the applied field affects only the
polarisation and it is independent of the energy in the field.
2. Calculate the energy in an electric field with flux density 6 units and field intensity of 4
units.
a) 12
b) 24
c) 36
d) 48
View Answer
Answer: a
Explanation: The energy in an electric field is given by, W = 0.5 x D x E, where D = 6
and E = 4. We get W = 0.5 x 6 x 4 = 12 units.
3. Calculate the energy in an electric field with permittivity of 56 and field intensity of
36π(in μJ)
a) 3.16
b) 5.16
c) 7.16
d) 9.16
View Answer
Answer: a
Explanation: The energy in an electric field is given by, W = 0.5 x D x E. Since D = εE,
we get W = 0.5 x ε x E2
. On substituting the data, we get 3.16 microjoule.
4. Equipotential surface is a
a) Real surface
b) Complex surface
c) Imaginary surface

d) Not existing surface
View Answer
Answer: c
Explanation: Equipotential surface is an imaginary surface in an electric field of a given
charge distribution in which all the points on the surface are at the same electric potential.
5. The work done in moving a test charge from one point to another in an equipotential
surface is zero. State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: Since the electric potential in the equipotential surface is the same, the work
done will be zero.
6. When curl of a path is zero, the field is said to be conservative. State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: By Stoke’s theorem, when curl of a path becomes zero, then
∫ E.dl = 0. In other words the work done in a closed path will always be zero. Fields
having this property is called conservative or lamellar fields.
7. If the electric potential is given, which of the following cannot be calculated?
a) Electrostatic energy
b) Electric field intensity
c) Electric flux density
d) Permittivity
View Answer

Answer: a
Explanation: Using potential, we can calculate electric field directly by gradient
operation. From E, the flux density D can also be calculated. Thus it is not possible to
calculate energy directly from potential.
8. Superconductors exhibit which of the following properties?
a) Ferromagnetism
b) Polarisation
c) Diamagnetism
d) Ferrimagnetism
View Answer
Answer: c
Explanation: Since superconductors have very good conductivity at low temperatures (σ-
>∞), they have nearly zero resistivity and exhibit perfect diamagnetism.
9. Debye is the unit used to measure
a) Permittivity
b) Electric dipole moment
c) Magnetic dipole moment
d) Susceptibility
View Answer
Answer: b
Explanation: Debye is the standard unit for measurement of electric dipole moment. 1
Debye = 3.336 x 10-30
Coulomb-meter.
10. Ceramic materials possess which of the following properties?
a) Brittle and low dielectric constant
b) Rigid and low dielectric constant
c) Brittle and high dielectric constant

d) Rigid and high dielectric constant
View Answer
Answer: c
Explanation: Ceramic materials are generally brittle. Since these materials are used in
capacitors, they have higher dielectric constant than polymer. With respect to energy,
they possess high electrostatic energy due to very high dielectric constant (W α ε).
“Electrostatic Properties”.
1. The permittivity is also called
a) Electrostatic energy
b) Dielectric constant
c) Dipole moment
d) Susceptibility
View Answer
Answer: b
Explanation: The term permittivity or dielectric constant is the measurement of
electrostatic energy stored within it and therefore depends on the material.
2. Dielectric constant will be high in
a) Conductors
b) Semiconductors
c) Insulators
d) Superconductors
View Answer
Answer: c
Explanation: Materials that have very less conductivity like ceramics, plastics have
higher dielectric constants. Due to their low conductivity, the dielectric materials are said
to be good insulators.

3. Under the influence of electric field, the dielectric materials will get charged
instantaneously. State True/False.
a) True
b) False
View Answer
Answer: a
Explanation: The dielectrics have the ability of storing energy easily when an electric
field is applied as their permittivity is relatively higher than any other materials.
4. Insulators perform which of the following functions?
a) Conduction
b) Convection
c) Provide electrical insulation
d) Allows current leakage at interfaces
View Answer
Answer: c
Explanation: Insulators is a non-conducting material which prevents the leakage of
electric current in unwanted directions. Thus it is used to provide electrical insulation.
5. Which of the following properties distinguish a material as conductor, insulator and
semiconductor?
a) Free electron charges
b) Fermi level after doping
c) Energy band gap
d) Electron density
View Answer
Answer: c
Explanation: The only parameter that classifies the material as conductor or insulator or
semiconductor is the band gap energy. It is the energy required to make the electrons

conduct. This is low of conductors, average for semiconductors and very high for
insulators. This means it requires very high energy to make an insulator conduct.
6. Semiconductors possess which type of bonding?
a) Metallic
b) Covalent
c) Ionic
d) Magnetic
View Answer
Answer: b
Explanation: Conductors exhibit metallic bonding. Insulators exhibit ionic bonding and
semiconductors exhibit covalent bonding due to sharing of atoms.
7. Find the susceptibility of a material whose dielectric constant is 2.26.
a) 1.26
b) 3.26
c) 5.1
d) 1
View Answer
Answer: a
Explanation: Electric susceptibility is the measure of ability of the material to get
polarised. It is given by, χe = εr – 1.Thus we get 1.26.
8. The bound charge density and free charge density are 12 and 6 units respectively.
Calculate the susceptibility.
a) 1
b) 0
c) 2
d) 72
View Answer

Answer: c
Explanation: The electric susceptibility is given by, χe = Bound free density/Free charge
density. χe = 12/6 = 2. It has no unit.
9. The susceptibility of free space is
a) 1
b) 0
c) 2
d) ∞
View Answer
Answer: b
Explanation: For free space/air, the relative permittivity is unity i.e, εr = 1. Thus χe = εr –
1 = 0. The susceptibility will become zero in air.
10. When the electric field becomes zero, which of the following relations hold good?
a) E = P
b) D = P
c) B = P
d) H = P
View Answer
Answer: b
Explanation: The electric flux density of a field is the sum of εE and polarisation P. It
gives D = εE + P. When electric field becomes zero, it is clear that D = P.
“Conductors”.
1. Which of the following are conductors?
a) Ceramics
b) Plastics
c) Mercury

d) Rubber
View Answer
Answer: c
Explanation: Normally, metals are said to be good conductors. Here mercury is the only
metal (which is in liquid form). The other options are insulators.
2. Find the range of band gap energy for conductors.
a) >6 eV
b) 0.2-0.4 eV
c) 0.4-2 eV
d) 2-6 eV
View Answer
Answer: b
Explanation: Conductors are materials with least band gap energy. The smallest range in
this group is 0.2-0.4 eV.
3. Conduction in metals is due to
a) Electrons only
b) Electrons and holes
c) Holes only
d) Applied electric field
View Answer
Answer: a
Explanation: Conduction in metals is only due to majority carriers, which are electrons.
Electrons and holes are responsible for conduction in a semiconductor.
4. Find the band gap energy when a light of wavelength 1240nm is incident on it.
a) 1eV
b) 2eV
c) 3eV

d) 4eV
View Answer
Answer: a
Explanation: The band gap energy in electron volt when wavelength is given is, Eg =
1.24(μm)/λ = 1.24 x 10-6
/1240 x 10-9
= 1eV.
5. Alternating current measured in a transmission line will be
a) Peak value
b) Average value
c) RMS value
d) Zero
View Answer
Answer: c
Explanation: The instantaneous current flowing in a transmission line, when measured
using an ammeter, will give RMS current value. This value is 70.7% of the peak value.
This is because, due to oscillations in AC, it is not possible to measure peak value. Hence
to normalise, we consider current at any time in a line will be the RMS current.
6. The current in a metal at any frequency is due to
a) Conduction current
b) Displacement current
c) Both conduction and displacement current
d) Neither conduction nor displacement current
View Answer
Answer: a
Explanation: At any frequency, the current through the metal will be due to conduction
current. Only at high frequencies and when medium is air, the conduction is due to
displacement current. Thus in general the current in metal is due to conduction current,
which depends on the mobility of the carriers.

7. For conductors, the free electrons will exist at
a) Valence band
b) Middle of valence and conduction band
c) Will not exist
d) Conduction band
View Answer
Answer: d
Explanation: In conductors, the free electrons exist in the conduction band. Since the
band gap energy is very low, less energy is required to transport the free electrons to the
conduction band, as they are readily available to conduct.
8. The current flowing through an insulating medium is called
a) Conduction
b) Convection
c) Radiation
d) Susceptibility
View Answer
Answer: b
Explanation: A beam of electrons in a vacuum tube is called convection current. It occurs
when current flows through an insulating medium like liquid, vacuum etc.
9. Find the conduction current density when conductivity of a material is 500 units and
corresponding electric field is 2 units.
a) 500
b) 250
c) 1000
d) 2000
View Answer

Answer: c
Explanation: The conduction current density is given by, J = σE
J = 500 X 2 = 1000 units.
10. Calculate the convection current when electron density of 200 units is travelling at a
speed of 12m/s.
a) 16.67
b) 2400
c) 2880
d) 0.06
View Answer
Answer: b
Explanation: The convection current density is given by, J = ρeV
J = 200 X 12= 2400 units.
“Dielectrics”.
1. A dielectric is always an insulator. But an insulator is not necessarily a dielectric. State
True/False.
a) True
b) False
View Answer
Answer: a
Explanation: For a material to be dielectric, its permittivity should be very high. This is
seen in insulators. For a material to be insulator, the condition is to have large band gap
energy. However, this is not necessary for a dielectric.
2. Identify a good dielectric.
a) Iron
b) Ceramics
c) Plastic

d) Magnesium
View Answer
Answer: b
Explanation: Iron and magnesium are metals. Hence they need not be considered. Both
ceramics and plastic are insulators. But dielectric constant is more for ceramics always.
Hence ceramics is the best dielectric.
3. A dielectric can be made a conductor by
a) Compression
b) Heating
c) Doping
d) Freezing
View Answer
Answer: b
Explanation: On increasing the temperature, the free electrons in an insulator can be
promoted from valence to conduction band. Gradually, it can act as a conductor through
heating process. This condition is called dielectric breakdown, wherein the insulator loses
its dielectric property and starts to conduct.
4. Find the dielectric constant for a material with electric susceptibility of 4.
a) 3
b) 5
c) 8
d) 16
View Answer
Answer: b
Explanation: The electric susceptibility is given by χe = εr – 1. For a susceptibility of 4,
the dielectric constant will be 5. It has no unit.

5. For a dielectric which of the following properties hold good?
a) They are superconductors at high temperatures
b) They are superconductors at low temperatures
c) They can never become a superconductor
d) They have very less dielectric breakdown voltage
View Answer
Answer: b
Explanation: Superconductors are characterised by diamagnetism behaviour and zero
resistivity, which true for a dielectric. They occur only at low temperature. Thus a
dielectric can become a superconductor at low temperatures with very high dielectric
breakdown voltage.
6. The magnetic field which destroys the superconductivity is called
a) Diamagnetic field
b) Ferromagnetic field
c) Ferrimagnetic field
d) Critical field
View Answer
Answer: d
Explanation: Critical field is that strong magnetic field which can destroy the
superconductivity of a material. The temperature at which this occurs is called transition
temperature.
7. The magnetic susceptibility in a superconductor will be
a) Positive
b) Negative
c) Zero
d) Infinity
View Answer

Answer: b
Explanation: Due to perfect diamagnetism in a superconductor, its magnetic
susceptibility will be negative. This phenomenon is called Meissner effect.
8. The superconducting materials will be independent of which of the following?
a) Magnetic field
b) Electric field
c) Magnetization
d) Temperature
View Answer
Answer: b
Explanation: Superconducting materials depends only on the applied magnetic field,
resultant magnetization at the temperature considered. It is independent of the applied
electric field and the corresponding polarization.
9. Find the mean free path of an electron travelling at a speed of 18m/s in 2 seconds.
a) 9
b) 36
c) 0.11
d) 4.5
View Answer
Answer: b
Explanation: The mean free path is defined as the average distance travelled by an
electron before collision takes place. It is given by, d = v x τc, where v is the velocity and
τc is the collision time. Thus d = 18 x 2 = 36m.
10. Find the velocity of an electron when its kinetic energy is equal to one electron volt
(in 105
m/s).
Given charge of an electron e = 1.6 x 10-19
and mass of an electron m = 9.1 x 10-31
.
a) 3.9

b) 4.9
c) 5.9
d) 6.9
View Answer
Answer: c
Explanation: When the kinetic energy and one electron volt are equal, we can equate
mv2
/2 = eV. Put e and m in the equation to get velocity v = 5.9 x 105
m/s.
“Displacement and Conduction Current”.
1. Find the conductivity of a material with conduction current density 100 units and
electric field of 4 units.
a) 25
b) 400
c) 0.04
d) 1600
View Answer
Answer: a
Explanation: The conduction current density is given by, Jc = σE. To get conductivity, σ
= J/E = 100/4 = 25 units.
2. Calculate the displacement current density when the electric flux density is 20sin 0.5t.
a) 10sin 0.5t
b) 10cos 0.5t
c) 20sin 2t
d) 20cos 2t
View Answer
Answer: b
Explanation: The displacement current density is given by, Jd = dD/dt.
Jd = d(20sin 0.5t)/dt = 20cos 0.5t (0.5) = 10cos 0.5t.

Electromagnetic Theory Multiple Choice Questions

Electromagnetic Theory Multiple Choice Questions

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