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).

EASY

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Assertion: When two charges are brought close to each other, potential energy of the system may increase or decrease.

Reason: When work done by a conservative force is positive, the potential energy of the system increases, and when work done by a conservative force is negative, the potential energy of the system decreases.

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Important Questions on Electrostatic Potential and Capacitance

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

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

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

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

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

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>Electrostatic Potential and Capacitance>Potential due to System of Charges

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?

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

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:

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

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.

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

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>Electrostatic Potential and Capacitance>Potential due to System of Charges

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>Electrostatic Potential and Capacitance>Potential due to System of Charges

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:

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

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:

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

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?

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

Four point charge (with equal magnitude of charge of $5 C;$ but with different signs) are placed at four corners of a square of side $10 m .$ Assuming that the square is centered at the origin and the configuration of the charges are as given in the figure, the potential and the magnitude of electric field at the origin, respectively are

[Note $k = \frac{1}{4 π ε_{0}}]$

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

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:

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

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?

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

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

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

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

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

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

Question Image

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

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)

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

Van de Graaff generator consists of a hollow metal sphere of diameter $2 m$ . If the potential on the surface of the sphere is $6$ million volt, the charge accumulated over the surface of the sphere is:

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential due to System of Charges

N

number of charges,

+ Q

each, are placed maintaining equal distance on the circumference of a circle of radius

R .

The net electrostatic potential at the centre of the circle is

Important Questions on Electrostatic Potential and Capacitance

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