Question paper of Pre-University Examination of Electromagnetic Field Theory held at Guru Nanak Education Trust Group of Institution, Roorkee in EVEN Semester Session: 2012-13

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GURU NANAK EDUCATION TRUST GROUP OF INSTITUTION
ELECTROMAGNETIC FIELD THEORY (TEC-401)
PRE-UNIVERSITY EXAMINATION
Session: 2012-13 / EVEN SEMESTER
B.TECH (ECE) 2
nd
Year
Write down your Roll No on the Question paper. M.M. 100
Attempt All Questions. Time: 2.30 Hr
1. Attempt any four questions
a. If A = 10 ax – 4 ay + 6 az and B = 2 ax + ay, find (i) the
component of A along ay, (ii) the magnitude of 3A – B,
(iii) a unit vector along A + 2B.
b. Three field quantities are given by
P = 2 ax – az
Q = 2 ax – ay + 2 az
R = 2 ax – 3 ay + az
Determine
i. ( P + Q ) X ( P – Q )
ii. P . Q X R
iii. A unit vector perpendicular to both Q and R
c. Given that F = x2
ax – xz ay – y2
az , calculate the
circulation of F around the closed path
d. Determine the gradient of the following scalar fields:
i. U = x2
y + xyz
Roll No. +

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ii. V = ρ z sinφ + z2
cos2
φ + ρ2
iii. F = cosθ sinφ ln(r) + r2
φ
e. If r is the position vector of a point, then evaluate
i. Grad ( r )
ii. Grad ( 1 / r )
f. Transform the following vector to spherical
coordinates. The vector is A = 5 ax
)
2. Attempt any four questions
a. The finite sheet 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 on the z = 0 plane
has a charge density ρs = xy ( x2
+ y2
+ 25 )3/2
nC/m2
.
Find
i. The total charge on the sheet
ii. The electric field at (0, 0, 5)
iii. The force experienced by a -1 mC charge located at
(0, 0, 5)
b. Given the potential sinθ cosφ
i. Find the electric flux density D at (2, π/2, 0).
ii. Calculate the work done in moving a 10
) )
c. Derive dielectric – dielectric boundary conditions.
d. Explain convection current and conduction current.
Derive ohm’s law in point form.
e. Two extensive homogeneous isotropic dielectrics meet
on a plane z = 0. For z > 0, εr1 = 4 and for z < 0, εr2 = 3. A
uniform electric field E1 = 5 ax – 2 ay + 3 az kV/m exists
for z ≥ 0. Find
i. E2 for z ≤ 0
ii. The energy densities (in J/m3) in both dielectrics
f. Find the electric flux density at point P (6, 4, -5) caused
by a uniform line charge ρL = 20 μC/m on z-axis.
3. Attempt any four questions
a. Explain Biot-savart law and ampere’s circuit law.
b. The conducting triangular loop In fig. carries a current
of 10 A. Find H at (0, 0, 5) due to side 3 of the
triangular loop.
c. Planes z = 0 and z = 4 carry current K = -10 ax A/m and
K = 10 ax A/m respectively. Determine H at
i. (1, 1, 1)
ii. (0, -3, 10)
d. A charged particle of mass 2 kg and charge 3 C starts at
point (1, -2, 0) with velocity 4 ax + 3 az m/s in an
electric field 12 ax + 10 ay V/m. At time t = 1 s,
determine
i. The acceleration of the particle
ii. Its velocity
iii. Its kinetic energy
e. What are inductors? Define inductance.
f. Define:
i. Magnetic dipole and magnetic dipole moment.
ii. Magnetization (M)
4. Attempt any two questions
a. Define the following:
i. Skin depth
ii. Intrinsic depth
iii. Phase velocity
iv. Pointing vector
b. (i) Explain Faraday law and Maxwell’s equations.
(ii) Explain wave propagation in lossy dielectrics.

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c. How the wave propagation takes place in dispersive
medium? Light is incident from air to glass at
Brewsters angle. Determine the incident and
transmitted angles.
5. Attempt any two questions
a. Derive transmission line differential equation. Derive
the condition of lossless transmission from it.
b. Derive input impedance of transmission line. Define
standing wave ratio?
c. Define:
i. Reflection coefficient
ii. Propagation constant
Answers:
1. (a)
i. The component of A along ay is Ay = -4.
ii. 3 A – B = 28 ax – 13 ay + 18 az.
iii. A unit vector along A + 2 B = 0.9113 ax – 0.1302 ay +
0.3906 az.
1. (b)
i. (P + Q) X (P - Q) = 2 ax +12 ay + 4 az
ii. P. (Q X R) = 14.
iii. +- (0.745 ax + 0.298 ay – 0.596 az)
1. (c)
1. (d)
i. y (2x + z) ax + x (x + z) ay + xy az.
ii. (z Sinφ + 2ρ) aρ + (2 cosφ – z2
/ρ Sin2φ) aφ + (ρ Sinφ + 2z
Cos2
φ) az.
iii. (Cosθ Sinφ/r + 2ρφ) aρ – Sinθ Sinφ/r ln(r) aθ + (Cotθ
Cosφ ln(r)/r + r Cosecθ) aφ.
1. (e)
i.
ii.
1. (f) A = -1.057 ar – 2.27 aθ – 4.33 aφ
2. (a)
i. Q = 33.15 nC
ii. E = (-1.5 ax – 1.5 ay + 11.25 az) V/m
iii. F = (1.5 ax + 1.5 ay - 11.25 az)mN
2. (b)
i. D = 2.5 ε0 ar C/m2
= 22.1 ar pC/m2
ii. W = 28.125 μ J
2. (e)
i. E2 = 5 ax – 2 ay + 4 az kV/m
ii. WE1 = 672 μ J/m3
WE2 = 597 μ J/m3
2. (f) D = (0.37 ax + 0.25 ay) μC/m2
3. (b) H = (-30.63 ax + 30.63 ay) mA/m
3. (c)
i. H = 10 ay A/m
ii. H = 0 A/m
3. (d)
i. a = 18 ax + 15 ay
ii. u = (22 ax + 15 ay + 3 az) m/s (At t = 1)
iii. K.E. = 718 J