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 solid conducting sphere having a charge $Q$ is surrounded by a charged concentric conducting hollow spherical shell. Let the potential differences 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 $- 3 Q,$ the new potential differences between the same two surfaces is

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Important Questions on Electrostatics

MEDIUM

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

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 Difference

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 Difference

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 Difference

Four point charges

- Q, - q, 2 q

and

2 Q

are placed, one at each corner of the square. The relation between

Q

and

q

for which the potential at the centre of the square is zero is

EASY

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

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)

EASY

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

The diagrams below show regions of equipotential.

Question Image

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

MEDIUM

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

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 Difference

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 Difference

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 Difference

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:

MEDIUM

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

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:

HARD

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

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 Difference

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

HARD

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

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