The diagrams below show regions of equipotential. A positive charge is moved from A to B in each diagram.

In all the four cases the work done is the same.

Maximum work is required to move q in figure (c).

Minimum work is required to move q in figure (a).

Maximum work is required to move q in figure (b).

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A point charge is placed at a distance $r$ from the centre of a conducting neutral sphere of radius $R (r > R)$ . The potential at any point $P$ inside the sphere at a distance $r_{1}$ from the point charge due to the induced charge of the sphere is given by $[k = \frac{1}{4 {πε}_{0}}]$

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Important Questions on Electrostatics

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at

P

, in the region, is found to vary between the limits

589.0 V

589.8 V

. What is the potential at a point on the sphere whose radius vector makes an angle of

60 °

with the direction of the field?

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

A metallic sphere is kept in between two oppositely charged plates. The most appropriate representation of the field lines is

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

An electron with an initial speed of

4 .0 \times 10^{6} m s^{- 1}

is brought to rest by an electric field. The mass and charge of an electron are

9 \times 10^{- 31} kg

and

1.6 \times 10^{- 19} C

, respectively. Identify the correct statement.

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

A certain p-n junction having a depletion region of width

20 μm,

was found to have a breakdown voltage of

100 V

. If the width of the depletion region is reduced to

1 μm

during its production, then it can be used as a zener diode for voltage regulation of:

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

If potential(in

volts

) in a region is expressed as

V (x, y, z) = 6 x y - y + 2 y z

, the electric field(in

N C^{- 1}

) at point

(1, 1, 0)

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

Consider a spherical shell of radius

R

with a total charge

+ Q

uniformly spread on its surface (center of the shell lies at the origin

x = 0

). Two point charge,

+ q a n d - q

are brought, one after the other, from far away and placed at

x = - \frac{a}{2} a n d x = + \frac{a}{2} (a < R),

respectively. Magnitude of the work done in this process is

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

Two equal charges of magnitude

Q

each are placed at a distance

d

apart. Their electrostatic energy is

E . A .

third charge

- \frac{Q}{2}

is brought midway between these two charges. The electrostatic energy of the system is now?

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

Assume that an electric field

\vec{E} = 30 x^{2} \hat{i}

exists in space. Then the potential difference

V_{A} - V_{O}

, where V_O is the potential at the origin and V_A the potential at x = 2 m is :

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is :

Question Image

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

An electric field

\vec{E} = (25 \hat{i} + 30 \hat{j}) N C^{- 1}

exists in a region of space. If the potential at the origin is taken to be zero then the potential at

x = 2 m

y = 2 m

is:

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

The diagrams below show regions of equipotential.

Question Image

A positive charge is moved from $A$ to $B$ in each diagram.

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

Four equal point charges

Q

each are placed in the

x y

plane at

(0, 2), (4, 2), (4, - 2)

and

(0, - 2)

. The work required to put a fifth charge

Q

at the origin of the coordinate system will be:

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

Some equipotential surfaces are shown. The electric field at any point is

Question Image

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

A point particle of mass $0.5 kg$ is moving along the $X$ -axis under a force described by the potential energy $V$ shown below. It is projected towards the right from the origin with a speed $v$ .

Question Image

What is the minimum value of $v$ for which the particle will escape infinitely far away from the origin?

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

The electric potential at a point

(x, y)

in the

x

y

plane is given by

V = - K x y

The electric field intensity at a distance

r

from the origin varies as

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

A positive point charge is released from rest at a distance

r_{0}

from a positive line charge with uniform charge density. The speed

(v)

of the point charge, as a function of instantaneous distance

r

from line charge, is proportional to
Question Image

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

A solid conducting sphere, having a charge

Q,

is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be

V .

If the shell is now given a charge of

- 4 Q,

the new potential difference between the same two surfaces is:

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

Consider a cube of uniform charge density,

ρ

. The ratio of the electrostatic potential at the center of the cube to that at one of the corners of the cube is,

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

A charge

Q

is distributed over three concentric spherical shells of radii

a, b, c (a < b < c)

such that their surface charge densities are equal to one another.

The total potential at a point at distance

r

from their common centre, where

r < a,

would be:

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Potential and Potential Energy

When an

α

-particle of mass

m

moving with a undefined velocity bombards on a heavy nucleus of charge

Ze

, its distance of the closest approach from the nucleus depends on

m

as:

A point charge is placed at a distance r from the centre of a conducting neutral sphere of radius R r>R. The potential at any point P inside the sphere at a distance r1 from the point charge due to the induced charge of the sphere is given by k=14πε0

Important Questions on Electrostatics

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A point charge is placed at a distance $r$ from the centre of a conducting neutral sphere of radius $R (r > R)$ . The potential at any point $P$ inside the sphere at a distance $r_{1}$ from the point charge due to the induced charge of the sphere is given by $[k = \frac{1}{4 {πε}_{0}}]$