3'1ELECTRIC FIELDS

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3'1ELECTRIC FIELDS

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Title: 3'1ELECTRIC FIELDS

1
3.1 ELECTRIC FIELDS
3.1.1 Simple Electrostatics
3.1.2 Coulombs Law
3.1.3 Electric Field E
3.1.4 Electric Potential V
3.1.5 Gravitational Analogy
2
3.1.1 Simple Electrostatics
Electrostatics is the study of electric charges
, the between them and the
associated with them.

Electric charges
Electric charges are measured in , and
the charge of an electric is e, where e .
Electric charge is , i.e., it
occurs only in discrete amount.
In an isolated system, the net charge is a .
Insulators and conductors
All electrons in electrical insulators are to
their nuclei and the removal or addition of
electrons at one places cause the flow of
electrons elsewhere.
Electrical conductors have the
electrons that are around and the loss or
gain of electrons would cause a of
those left.

Charging an insulator
An insulator can be charged by , the process in
which the outermost shell electrons located near
the surfaces are transfered from one body to
another.
The excessive electric charge on the insulator is
then confined to the .
Charging an insulated conductor
An insulated conductor consists of a conductor
mounted on a or suspended from a .
Insulated conductors can be easily charged by an
.

Insulated conductors can also be charged by
electrostatic using an electrophorus.
An insulating sheet is initially charged by .
A (neutral) metal plate with an handle is
then placed on top of the sheet.
The insulating sheet then unlike charges to
the part of the metal plate.
The metal plate is then momentarily, so that
the upper charges are and this charge can be
transferred to another conductor.

Charge distribution in conductors
Inside a metal, charges are free to move
throughout. The mutual force pushes any
excessive charge apart until they meet the ,
where the electric force is balanced by the
force of the wall.
As a result, no charge can stay inside a metal
in electrostatic.
A charged conductor is effectively a of
charge in static state.
The is the radius of curvature, the higher is
the surface charge density (point action).

Steady state
6

The shuttling ball experiment
When the metal ball touches the positive plate,
say, it gains charges, and is then it.
On reaching the negative plate the ball loses its
charges and then gains charges. It is then
the negative plate.
The whole process is repeated indefinitely and
the ball between the two metal plates.
The balls are subjected to all the times
in the above experiment.

7
Examination questions

1990-IIA-27
A light conducting sphere is hanged from a long
insulating thread between oppositely charged
metal plates connected to a high voltage supply.
If the sphere is given a positive charge, it will
A. move to the positive plate and stick to it.
B. move to the negative plate and stick to it.
C. remain still.
D. oscillate, touching each plate in turn,
beginning with the negative plate.
E. oscillate, touching each plate in turn,
beginning with the positive plate.

1995-IIA-26
Two uncharged metal spheres, A and B, supported
by insulating stands are placed side by side but
not touching each other. A student places a
positively-charged rod near sphere A and he
touches sphere B with his finger momentarily.
When the rod is removed afterwards, what are the
signs of the charges induced on the spheres?
Sphere A Sphere B
A. positive neutral
B. negative negative
C. negative neutral
D. neutral positive
E. neutral negative

2001-IIA-20
Two insulated uncharged metal spheres X and Y
are in contact with each other. A positively
charged rod is brought near X without any contact
while sphere X is earthed as shown.
At steady state, which of the following
description is/are correct?
(1) Sphere X gains electrons.
(2) Sphere Y loses electrons.
(3) Sphere X acquires a negative electric
potential.
(4) Sphere Y acquires a positive electric
potential.
A. (1) only
B. (1) and (2) only
C. (1) and (3) only
D. (2) and (4) only
E. (1), (2), (3) and (4)

2005-IIA-12
P, Q and R are small identical metal spheres. P
and Q are fixed at a certain separation in vacuum
and they carry charges of the same magnitude.
The attractive force between them is F. Sphere R
is initially uncharged. It first touches P and
then it touches Q. What is the electrostatic
force between P and Q after R is taken away?
A. F/4 B. F/8 C. 3F/4 D. 3F/8

11
3.1.2 Coulombs Law

Statement of Coulombs law
The magnitude of the force between two static
point charge is proportional to the
of the charges, and proportional
to the of the distance
between them. Mathematically,
Eq.(1)
where ? is called the permittivity whose value
depends on the concerned.
The permittivity of a vacuum is denoted as ?o and
is called the , where
?o
or

Experimental test of Coulombs law
From the diagram, the deflection D .
By considering the equilibrium of the sphere A,
we have F , where T .
Therefore, F ? for small ?. Therefore, F
is approximately D.
Coulombs law is verified if it can be shown that
- , and
- .

13
Examination questions
14
3.1.3 Electric Field E

Electric field as a region
An electric field is a where an
experience an electric force.
An electric field can be established wherever
there are .
Electric field strength E
The electric field strength E at a point is
defined as the electric force F experienced per
unit positive test charge q placed at that point,
i.e.,
E Eq.(2)
Unit of electric field strength is .
We must imagine q to be very because we need
to know E before q was introduced into the field.

Electric field lines
An electric field line is a fictional concept
developed to aid the visualization of an . It
is imaginary, but it represents a real field.
The to a field line at a point gives the
direction of E at that point.
The of the field lines at a point is
porportional to the magnitude of E at that point.
The field lines begin from charges and end at
equal charges.
and field lines represent uniform
electric field.

Investigating electric field between parallel
metal plates using a charged foil strip
Observing electric field patterns produced by
electrodes of different shapes

E due to a point charge
By Coulumb's Law, the size of the electric force
on a test charge q placed at a distance r from
the source charge Q is
Thus the size of the electric field at a distance
r from Q is
Eq.(3)
The electric field lines are directed (for
ve Q) or (for ve Q) the point charge.

E due to a charged conducting sphere
Recall that a charged metal sphere is effectively
a thin of charge.
In electrostatics, the electric field strength at
any point inside the sphere must be ,
otherwise, free charges inside the conductor
would unduly move to the surface.
Outside the sphere, the field at any point is
exactly the same as if the whole charge were
concentrated at the of the sphere, i.e., the
size of the electric field is

Example
A point charge Q1 is placed at the centre of
a hollow conductor carrying a charge Q2 as
shown. The inner and outer radius of the
conductor are respectively a and b. Find the
field strengths for (i) r lt a, (ii) a lt r lt b,
(iii) r
gt b.

20
Examination questions

2005-IIA-34
The electric field strength near the surface of
a charged metal sphere is E. The charge on the
sphere and its radius are doubled. What is the
new electric field strength near the spheres
surface?
A. E/4 B. E/2 C. E D. 2E

21
3.1.4 Electric Potential V

Electric potential energy
If a positive charge q is moved from A to B in an
electric field as shown above, an has to
do work against the and thus energy has
to be the system.
As a result, the system an amount of
electrical potential energy equal to the work
done.
When the charge is allowed to return from B to A,
work is done by the and the electrical
potential energy previously is , say, as
the of the point charge.

Electric potential difference
The electrical potential difference between two
points A and B is defined as the per
unit charge moving from A to B, i.e.,
The unit of electrical potential difference is
.
Electric potential V
The electrical potential V at a point in an
electric field is defined as the per unit
charge moving from to that point
Electrical potential is a property of a
in the field.
Electrical potential is a quantity.
The electrical potential at infinity is .
Positive charges naturally move from places of
electrical potential to electrical potential.

Equipotentials
An equipotential surface is an imaginary surface
all the points on which have the same .
When a charge moves on such a surface, energy
change occurs and work is done. The force due
to the field must therefore act at to the
surface at any point. So equipotential surfaces
(or lines in 2D) and field lines are always at
.
Since equipotential surfaces are drawn at every
equal potential difference, they are where
the electric field is stronger, since a
distance need to be travelled to perform the same
amount of work in such region.
The surface of a conductor in electrostatic must
be an since on the surface.

Plotting equipotential lines
A potential difference is applied through two
electrodes across a slightly conducting surface
such as iridium oxide surface.
The potential difference across any two points is
detected by a .
When the galvanometer shows deflection, the
two points are at the same .
The exact potential relative to the negative
terminal at a point on the conducting surface can
be measured by a .

V due to a point charge
The total work W to bring a test charge q from
infinity to to a distance r is
Where F ,according to Coulombs law, thus
The potential V is therefore obtained by V
, i.e.,
Eq.(4)

The potential distribution for a positive point
charge looks like a , and a positive test
charge tends to or it.
The potential distribution for a negative point
charge looks like a , and a positive test
charge tends to or it.

V
27

V due to a charged conducting sphere
Outside the sphere, the conductor has the same
electric field as that of a point charge at its
, so
Inside the sphere, since E , the potential
remains a that equals the potential at the ,
i.e.,

Relation between V and E
If a charge q moves a very short distance dr in
the direction of E, the differential work done dW
by the electric force is
dW
If the p.d. between the two points is dV, we have
by definition,
dV
Therefore, in differential form, V and E are
related as
Eq.(5)
The size of E is obtained from the of
the V-r graph.
In integral form, we have Eq.(6)

V due to two oppositely charged parallel plates
Since the electric field between two oppositely
charged parallel plates is , the potential
gradient is a .
The electric potential at x is obtained
graphically as
V(x)
The potential difference Vd between the plates is
Vd Eq.(7)

Example
Two identical parallel plates separated at 0.9 m
are charged by an EHT at 6 V with the negative
plate earthed. A metal slab 0.3 m thick is now
inserted mid-way between the plates in two cases
(i) the plates are connected to the EHT during
the insertion, and
(ii) the plates are disconnected from the EHT
during the insertion.
Sketch the V-r graph after the insertion in the
two cases.
(i) (ii)

Example
A point charge Q1 is placed at the centre of a
hollow conductor carrying a charge Q2 as shown.
The inner and outer radius of the
conductor are respectively a and b. Find the
potential for (i) r lt a, (ii) a lt r lt b, (iii) r
gt b.

32
Examination questions

1990-IIA-28
The arrangement above shows two concentric
hollow
metal spheres of inner radius b and outer radius
a. A
charge Q is given to the inner sphere and the
outer
sphere is earthed. What is the work done in
bringing
a small positive charge q from infinity to the
surface of
the inner sphere?
A. zero B. C. D.
E.
1990-IIA-29
A uniformly charged wire has the form of a
circular
loop of radius b. P1 and P2 are two points
on the
axis of the loop. P1 is at a distance b from
the loop
centre and P2 is at a distance 2b from the loop
centre.
At P1, P2, the potentials are V1, V2
respectively. V2/V1 is equal to
A. 1/3 B. 2/5 C. 1/2 D.
?2/?5 E. 4?

1991-IIA-31
Which of the graphs below best represents the
variation of electrical potential V with distance
r from the centre of a charged hollow metal
sphere of external radius a?
A. B. C.
D. E.
1992-IIA-27
How do the two physical quantities below change
along the direction indicated by an electric
field line from a point positive charge?
(1) electric field intensity
E (2) potential V
A. Only E will increase B. Only V will
increase
C. Both E and V will increase D. Both E and V
will decrease
E. Both E and V will remain constant

1993-IIA-28
An uncharged metal sphere is placed in a uniform
electric field. Which of the following best
represents the electric field around the metal
sphere?
A. B. C.
D. E.
1993-IIA-29
A positively-charged metal sphere A of radius a
is joined by a conducting wire to an uncharged
metal sphere B of radius b placed far away from
the first sphere. The ratio of the surface
charge density on sphere A to that on the sphere
B is
A. b/a B. b2/a2 C. a/b D. a2/b2 E.
?(b/a)

1993-IIA-35
Two insulated parallel metal plates are
connected to the terminals of an EHT. When a
charged aluminium foil strip is placed between
the plates, deflection of the foil is observed as
shown.
Which of the following statements is/are true?
(1) The charge on the foil is negative.
(2) Deflection of the foil increases if the
separation between the plates decreases.
(3) When moving the foil towards the positive
plate, the deflection of the foil increases.
A. (1) only B. (3) only C. (1) and
(2) only
D. (2) and (3) only E. (1), (2) and (3)

1994-IIA-24
X, Y are two different points in an electric
field. A small charged object is released from
rest at X. Which of the following conditions
would ensure that the charged object will NOT
pass through Y?
A. The electric field at Y is zero.
B. The electric field at Y is stronger than that
at X.
C. The electric field between X and Y is not
zero.
D. The electric potentials at X and Y are equal.
E. The electric potential difference between X
and Y is not zero.
1994-IIA-27
The electric potential energy of a system of
charges at infinitely large distances from one
another is taken to be zero. What is the
electric potential energy stored in a system of
four charges, each of 1C, placed at the vertices
of a square with length of side 1 m?
(?o permittivity of vacuum)
A. 3/??o B. 1/??o(1 1/?2) C.
1/??o
D. 5/4??o E. 1/4??o(4 ?2)

1995-IIA-27
A, B, C, D are four points on a straight line as
shown. A point charge Q is fixed at A. When
another point charge Q is moved from B to C,
which of the following quantities will increase?
(1) The electric potential energy of the system
of charges.
(2) The magnitude of the electric field strength
at the point D.
(3) The electric potential at the point D.
A. (1) only B. (3) only C. (1) and (2)
only
D. (2) and (3) only E. (1), (2) and (3)

1996-IIA-16
The straight lines in the diagram
represent electric
field lines. Which of the following statements
about
this electric field is/are correct?
(1) A stationary negative charge placed at Q
tends to move to P.
(2) The electric field strength at P is stronger
than that at Q.
(3) Work has to be done in moving a negative
charge from R to P.
A. (1) only B. (3) only C. (1) and (2)
only
D. (2) and (3) only E. (1), (2) and (3)
1996-IIA-23
Five identical point charges, each of charge Q,
are fixed evenly on a circle of radius r. How
much work has to be done to bring another point
charge Q from infinitely to the centre of the
circle?
(?o permittivity of vacuum)
A. zero B. 5Q/4??or C.
5Q2/4??or
D. 5Q2/4??or2 E. 5Q/4??or2

1997-IIA-22
A metal sphere is charged to a potential of 100
V. If the charge density on its surface is 6 ?
10-9 Cm-2, find the radius of the sphere.
(Given permittivity of free space 8.85 ?
10-12 Fm-1)
A. 0.04 m B. 0.15 m C. 0.21 m D.
0.35 m E. 0.60 m
1997-IIA-28
A charged particle is accelerated across the gap
between two parallel metal plates maintained at a
certain potential difference in a vacuum.
Assuming there is no gravitational force, the
energy acquired by the charged particle in
crossing the gap depends on
(1) the mass of the charged particle.
(2) the width of the gap.
(3) the potential difference between the
plates.
A. (1) only B. (3) only C. (1) and
(2) only
D. (2) and (3) only E. (1), (2) and (3)

1999-IIA-21
Which of the following statements about electric
field lines is incorrect?
A. They are closest where the field is
strongest.
B. They are always perpendicular to
equipotential lines.
C. They always point from high electric
potential to low electric potential.
D. Work has to be done in moving an electron
along the direction of a field line.
E. They tend to attract one another.

2000-IIA-21
In the above arrangement, two small test charges
q and 2q are brought from infinity to the
positions shown. The two charges are collinear
with another charge Q and their mutual
separation is d. Which of the following
statements is/are correct?
(1) Charge q is at a higher potential than
charge 2q.
(2) The work done in bringing the charges q
and 2q from infinity to their respective
positions is the same.
(3) The potential energy of the system would
increase if d decreases.
A. (1) only B. (3) only C. (1) and
(2) only
D. (2) and (3) only E. (1), (2) and (3)

2000-IIA-22
The above figure shows a pattern of electric
field lines in which P, Q and R are points marked
on one of the field lines with PQ QR. If the
potential at P is 0 V, which of the following can
give the possible potential at Q and at R?
Potential at Q Potential at R
A. 200 V 450 V
B. 200 V 400 V
C. 200 V 350 V
D. 200 V 350 V
E. 200 V 450 V

2000-IIA-26
Two parallel plates are connected to an E.H.T.
of 4.5 kV. Electric breakdown occurs when the
separation of the plates is reduced to 1.5 mm.
Estimate the maximum acceleration of an electron
between the plates. (Given charge of an
electron 1.6 ? 10-19 C, mass of an electron
9.1 ? 10-31 kg)
A. 4.0 ? 107 m s-2 B. 1.0 ? 109 m s-2 C. 1.2
? 1012 m s-2
D. 1.6 ? 1015 m s-2 E. 5.3 ? 1017 m s-2
2002-IIA-20
In the above figure the solid lines represent
part of
an electric field due to a fixed point charge
Q (not
shown in the figure). A charged particle q,
subjected
only to electric force in the field, travels
along the dotted
curve shown. Which of the following conclusions
can be drawn?
A. q is travelling from X to Y.
B. The charge of q has the same sign as that of
Q.
C. q has a greater speed at X than at Y.
D. The electric potential at X due to Q is
higher than that at Y.

2003-IIA-24
In the figure, the solid curves are concentric
circles
representing a set of equipotentials surfaces in
an
electric field. The dotted curve ABC represents
the
path of a charged particle moving in the field.
Which
of the following deductions from the figure
is/are correct?
Neglect the effects of gravity.)
(1) The charged particle is always repelled from
the center of the concentric circles.
(2) The speed of the charged particle at A is
equal to that at C.
(3) The kinetic energy of the charged particle
at B is greater than that at A.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only

2003-IIA-32
In the figure, the dotted part represents a
spherical metallic shell A of uniform thickness.
The shell is neutral as a whole. A small
positively charged object B is placed inside the
cavity of the shell but not exactly at its
centre. Positive and negative charges are then
induced in the shell. (Distribution of induced
charges is not indicated.)
Which of the following statements is/are correct
when electrostatic equilibrium is reached?
(1) Positive induced charges are distributed
uniformly on the outer surface of the shell.
(2) The electric field at any point within the
cavity is zero.
(3) The electric potential at the outer surface
of the shell is higher than that at its inner
surface.
A. (1) only B. (2) only C. (1) and (3)
only
D. (2) and (3) only

2004-IIA-16
In the above figure, a point charge Q is placed
at A. The resulting electric potential at B is V.
If a point charge 2Q is now placed at C, the
mid-point between A and B, what is the electric
potential at B produced by both point charges?
(Assume that the electric potential at infinity
is zero.)
A. 4 V B. 3 V C. 2 V D. 0
2004-IIA-18
A positively charged particle is projected
with a certain
initial velocity into the electric field due to
a charge fixed at
O. Part of its trajectory (curve AB) is
sketched as shown.
Which of the following deductions is correct?
A. The trajectory must be a part of an ellipse.
B. The acceleration of the particle at B is
greater than that at A.
C. The kinetic energy of the particle at B is
greater than that at A.
D. The electrical potential energy of the
particle at B is greater than that at A.

2005-IIA-16
A negatively charged oil drop is kept stationary
between two horizontal metal plates connected to
a d.c. supply as shown. The oil drop then
acquires an additional negative charge. Which of
the following changes will be able to hold the
oil drop stationary?
(1) Disconnecting the plates from the supply and
moving the plates closer
(2) Keeping the separation between the plates
unchanged and increasing the p.d. between the
plates
(3) Keeping the p.d. between the plates
unchanged and moving the plates further apart
A. (1) only B. (3) only
C. (1) and (2) only D. (2) and (3) only

Measuring V at a point in space
The potential at a point in space can be
measured using a and a using the set
up as shown below.

Questions
What cant the potential be measured by a
voltmeter or a CRO?
What is the purpose of neutralizing the needle
probe?
Why cant the needle probe be neutralized by
earthing?
How can the potential be read out from the
experiment?
What is the major precaution in the experiment?

Effect of neighbouring bodies
The electric potential in space is generally
by a nearby positive body, but generally
by a nearby negative body.
When a neutral conductor is brought near to a
positively charged conducting sphere, the
potential near A is generally due to the
induction of charges at , while the
potential near C is generally due to the
induction of charges at .

51
3.1.5 Gravitational Analogy

Inverse square law of force
Coubombs law
Newtons law of universal gravitation
Field strength
Electric field strength E
(at a distance r from point charge Q)
Gravitational field strength g
(at a distance r from mass M)
Electric force in terms of E
(on a point charge q)
Gravitational force in terms of g
(on a mass m)

Field lines and equiopotentials
Gravitational field lines are always directed
the centre of a mass, while electric field
lines are directed from charge to charge.
Potential and potential energy
Electric potential
(at a distance r from point charge Q)
Gravitational potential
(at a distance r from mass M)
Electric potential energy in terms of electric
potential
(with a point charge q)
Gravitational potential energy in terms of
gravitational energy
(with a mass m)