BS Physics (Foundation) Series

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Module # 28
Electrostatic Potential & Flux Density
Electrostatics
The electricity at rest is called static electricity. The branch of
science which deals with the phenomena associated with
electricity at rest is known as electrostatics. Generally, an atom is
electrically neutral and the positive charge on proton is equal to
the negative charge on electron. When electrons are added to an
atom it becomes negatively charged and if the electrons are
removed from it, it becomes positively charged.
First Law of Electrostatics
Like charges repel, unlike charges attract.
Electrostatic Law
Electrostatic law states that a force exists between two charged
bodies and is directly proportional to the product of two charges
and inversely proportional to the square of the distance between
them.
F = C q1q2/r2.

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Law of Electrostatics
It is also known as Coulomb's law. It states that the force of
attraction or repulsion between two point charges is directly
proportional to their products and inversely proportional to the
square of distance between them, and inversely proportional to
the relative permittivity of the medium.
Units of charge smaller than coulomb are micro coulomb and pico
coulomb.
One micro coulomb = 10-6
Coulomb and
One pico coulomb = 10-12
Coulomb
For air or vacuum, Єr =1
Electrostatic Potential
In raising a body above the surface of the earth, the work has to
be done against the earth's gravitation and it increases its
gravitational potential energy. Now, if the body is released from
this height, it falls towards the earth.
If a positive charge is placed in an electric field, then, it will move
along the direction of field. On the other hand, if the positive
charge is made to move opposite to the direction of the electric
field, then, a force has to be applied and work has to be done on
the charge during its motion. This work is stored in the charge as

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an increase in electrostatic potential energy. This increase is due
to increase in electric potential of the charge.
If this charge is set free, then, it will move from a place or point at
higher potential to a point or place at lower potential and energy
equal to the difference of potentials of two points will be released.
In an electric field, a positive charge moves from a higher
potential to lower potential but a negative charge moves from
lower potential to higher potential.
Consider two points A and B at different potentials in an electric
field.
The potential difference between A and B is equal to the amount
of work done in carrying a unit positive charge from A to B against
the electric field. This work is denoted by WAB and the potential
difference is given by
VB – VA =VAB = WAB/q
where, q is a positive charge.
Unit of Electric Potential
Unit of electric potential in SI units is joule per coulomb or JC-1. It
is called volt.

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Electric Potential Difference
The work done in carrying a unit positive charge from one point to
another against electric field is known as electric potential
difference.
Just as difference in level determines the direction of flow of
water, pressure difference determines the direction of flow of gas
and temperature difference determines the direction of flow of
heat, similarly, the electric potential difference determines the
direction of flow of electric charge.
Electrostatic and Magnetic Force
Two point charges located at some distance apart interact with
each other with a force called as electrostatic force. The nature of
this force remains the same even if one of the two charges moves
in space or in any medium. But in case both the charges are in
motion, the nature of the force of interaction does not remain the
same. Instead a new force appears between them. This force,
which appears as a result of the interaction between two moving
charges, is known as magnetic force. The interaction of one
charge with some other charge is generally described by
associating fields around the charges. Just as an electric charge
brought in the field around a fixed charge interacts with the field
and experiences an electrostatic force, similarly, a moving charge

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interacts with a field around another moving charge and
experiences magnetic force.
Electrostatic Force
The electrostatic force between two charges can be calculated
with the help of Coulomb's law. Electrostatic force is attractive
between two dissimilar charges and it is repulsive between two
similar charges.
The force of repulsion between
(1) Proton and proton, &
(2) Electron and electron
is electrostatic force.
Similarly, the force of attraction between
(1) Positively charged nucleus and negatively charged electrons
revolving round the nucleus, &
(2) Positive proton and negative electron,
is electrostatic force.

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Electrostatic Induction
When a piece of paper is brought near a charged body, it is
attracted by it. The attraction of a neutral body by a charged body
can be explained on the basis of structure of atom.
When a charged body is brought close to a neutral body,
redistribution of charge takes place either in the body or on its
surface. This phenomenon is called electrostatic induction.
Explanation
The redistribution of charge in the neutral body exists only when
the charge is placed close to the body. If the charge is moved
away, then, the neutral body attains its original charge
distribution.
The redistribution of charge in the neutral body takes place due to
force of attraction or repulsion exerted by the charge on the
electrons of the atoms of the neutral body. It means that the
electrostatic induction is in accordance with the coulomb's law.
For further explanation, let us consider the following arrangement.
(1) Two metal spheres A and B fitted with wooden stands are
placed together so that they touch one another and form a single
conductor.

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Fig: Insulated uncharged conductors in contact
(2) A negatively charged ebonite (or polythene) rod is now
brought near the sphere A without touching it. As a result, a
positive charge appears on sphere A and a negative charge
appears on sphere B. This charge is called induced charge and
this phenomenon is called electrostatic induction.
Fig: +ve and -ve charges are induced on A and B respectively in
the presence of charged ebonite or polythene rod.
(3) Keeping the charged rod in the original position, the sphere
B is displaced away from A through a small distance.
Fig: A and B separated in presence of inducing charge

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(4) The charged rod is now removed and the spheres are tested
for charge by using an electroscope. A is found to be positively
charged and the B negatively charged.
Fig: When Inducing charge is removed, A and B have opposite
charges.
If we repeat the above experiment with the help of a positively
charged glass rod, then, sphere A will be negatively charged and
B will be positively charged.
From the above experiment, it is observed that when the charged
body is brought near to the neutral or uncharged body, then, the
opposite charge appears on the nearer end while the similar
charge appears on the remote end of the neutral or uncharged
body.
Gold Leaf Electroscope
An electroscope is a device used for detecting and testing an
electric charge.

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Construction and Working
It consists of a glass case that contains two thin leaves of gold
which can diverge away from each other. The leaves are attached
to a conductor (brass rod) which is connected to a metal ball
(sphere) or a disc outside the case. The leaves are insulated from
the glass case. If a charged object is brought close to the ball, two
types of charges appear, one on the disc or ball and the other on
the leaves (in accordance with electrostatic induction).
Fig: Charged Object brought close, giving rise to different charges
on ball & leaves
The two leaves share the same charge equally and repel each
other. If the ball is charged by touching it with the charged object,
the ball and the leaves acquire the same charge, i.e. physical
contact or nearness of the charged object plays major role in the
nature of charges appearing on ball and the leaves.

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Fig: Charged Object touched, giving rise to similar charges on ball
& leaves
In both the cases, greater the amount of charge, the greater
would be the divergence in leaves. To test the nature of charge
on a body, it is brought near a charged electroscope. If the charge
is the same as that on the electroscope, then, the divergence of
the leaves will increase. It decreases in case of opposite charge.
Electric Flux
For a uniform field and a plane surface, the electric flux ΦE is
defined to be the scalar product of the electric field vector E and
the plane surface area A.
For non-uniform fields and curved surfaces, we divide the
surfaces into very small patches of area ∆A called differential
area and assume that these are approximately flat and they are
so small that electric field E is almost uniform over it. For one of
these small patches of area, electric flux is defined by the relation
(differential form),

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∆ΦE = E. ∆A
For total flux for the whole surface, we add flux for each patch
such that
ΦE = ∑ E. ∆A
From the above relations, it is clear that electric flux is a scalar
quantity.
In terms of field lines, the flux is number of field lines passing
through a given surface.
In case of closed surfaces, the electric flux will be positive,
negative or zero in cases stated below:
(1) The electric flux is positive if net number of electric field lines
are leaving the surface, that is, there is a source of field lines in
the closed surface.
(2) The electric flux is negative if net number of electric field
lines are entering the closed surface or more field lines are
entering than leaving the surface, i.e. there is a sink of field lines
in the closed surface.
(3) The electric flux is zero if number of field lines entering are
equal to field lines leaving the surface.
Electric Flux through a Closed Surface

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The total electric flux through the closed surface will be
Φe = q / εo ------- (A)
Flux through any closed surface is the same as through a
spherical surface.
Eq. (A) shows that the electric flux through a closed surface
depends upon the medium and the charge enclosed by the closed
surface. It is to be noted that the result of Eq. (A) has nothing to
do with the shape or the geometry of the closed surface.
Flux Linkage
The flux linkage is the product of the number of turns and the
lines of flux linking them.
Flux Density
The Magnetic Field B is also called Flux Density.
Electric Flux Density
In an electric field the amount of flux passing through unit area at
right angle to the direction of the field is known as electric flux
density, denoted by symbol D. It is measured in coulomb per
square meter. It is also called the electric displacement.
Electric flux density is the amount of flux passing through a
defined area that is perpendicular to the direction of the flux.

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FLUX AND FLUX DENSITY
The magnetic flux across a surface is defined in analogy to the
electric flux used in Gauss's law. The total number of lines of
magnetic induction passing through a surface placed
perpendicular to the magnetic field is called the magnetic flux
through the surface and is denoted by Φ.
The SI unit of magnetic field B is Tesla which is equal to one
newton per ampere meter; hence the unit of magnetic flux can be
determined as
Φ = B.A = [(newton)/ (ampere meter)]. [meter2
] = NmA-1
The SI unit of flux (magnetic flux) is NmA-1
and is called weber
(Wb). The magnetic field B is also called flux density.
Let us consider an iron ring having a cross-sectional area of A
square meters and a mean circumference of 1 meters wound with
N turns carrying a current I amperes. Then
Total flux
ф = flux density x area = BA
Magnetic Flux
The total number of lines of magnetic induction passing through a

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surface placed perpendicular to the magnetic field is called the
Magnetic Flux through the surface and is denoted by Ф (Greek
letter phi).
The magnetic field or quantity of magnetic lines of force
surrounding a magnet taken as a whole is called magnetic flux. It
is denoted by symbol Ф (Greek letter phi). The number of lines of
force in a magnetic field determines the value of the flux. The
more lines of force, the greater the flux and the stronger the
magnetic field.
Alternatively, the space surrounding a magnet in which magnetic
force is exerted is called a magnetic field, and contains something
which we call magnetic flux.
The SI unit of magnetic flux is the Weber (Wb) and may be taken
as equal to 108
lines of force or flux-lines. The Weber is a very
large unit, sub units are often used: one milliweber (mWb) is
equal to 10-3
Wb and a microweber (μWb) equals 10-6
Wb.
Magnetic Flux Density
The number of lines of force per unit area is called the flux density
or it is the amount of flux per unit area in the magnetic field. It is
denoted by symbol B. The formula for flux density is given below
B = ф /A

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where ф is flux and A is the cross-sectional area of the magnetic
field. The SI unit of flux density is tesla (T). One tesla equals one
Weber per square meter (Wb/m2
).
Magnetic flux density is the magnetic flux per unit area in a
magnetic field. SI unit of flux density is Weber/m2
.
Magnetic flux density is the flux per unit area of a surface held
perpendicular to the magnetic field.