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).

A system of three charges are placed as shown in the figure: If D > > d , the potential energy of the system is best given by:

1 4 π ϵ 0 - q 2 d - q Q d D 2

1 4 π ϵ 0 + q 2 d + q Q d D 2

1 4 π ϵ 0 - q 2 d - q Q d 2 D 2

1 4 π ϵ 0 - q 2 d + 2 q Q d D 2

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Consider a metallic sphere of radius $R$ concentric with another hollow metallic sphere of inner radius $2 R$ and outer radius $3 R$ as shown in the figure. The inner,sphere is given a charge $- Q$ and outer $+ 2 Q$ . The electrostatic potential energy of the system is

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Important Questions on Electrostatics

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrical 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:

EASY

Physics>Electricity and Magnetism>Electrostatics>Electrical Potential Energy

Write the expression for magnetic potential energy of a magnetic dipole kept in a uniform magnetic field and explain the terms.

EASY

Physics>Electricity and Magnetism>Electrostatics>Electrical Potential Energy

An electric dipole of dipole moment is

6.0 \times 10^{- 6} C m

placed in a uniform electric field of

1.5 \times 10^{3} N C^{- 1}

in such a way that dipole moment is along electric field. The work done in rotating dipole by

180 °

in this field will be_______

mJ

HARD

Physics>Electricity and Magnetism>Electrostatics>Electrical 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?

HARD

Physics>Electricity and Magnetism>Electrostatics>Electrical Potential Energy

An electric dipole lies in an electric field

\vec{E} = 1000 \hat{i} N / C

in such a position that its dipole moment is

(12 \hat{i} + 5 \hat{j}) \times 10^{- 29} C - m .

It is rotated so that the dipole moment becomes

(- 12 \hat{i} + 5 \hat{j}) \times 10^{- 29} C - m .

The work done by the external agent is

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrical 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?

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrical Potential Energy

Define electric dipole moment. An electric dipole is placed within a uniform electric field $(E)$ and is rotated to an angle $θ = 180 °$ . Find out the work done.

EASY

Physics>Electricity and Magnetism>Electrostatics>Electrical Potential Energy

A system of two charges separated by a certain distance apart stores electrical potential energy. If the distance between them is increased, the potential energy of the system,

EASY

Physics>Electricity and Magnetism>Electrostatics>Electrical Potential Energy

A large metal plate has a surface charge density of

8.85 \times 10^{- 6} C m^{- 2}

. An electron having initial kinetic energy of

8 \times 10^{- 17} J

is moving towards the center of the plate. If the electron stops just before reaching the plate then the initial distance between the electron and the plate is [Take

ε_{0} = 8.85 \times 10^{- 12} C^{2} N m^{- 2}

]

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrical Potential Energy

Derive an expression for potential energy of an electric dipole placed in a uniform electric field.

EASY

Physics>Electricity and Magnetism>Electrostatics>Electrical Potential Energy

The diagrams below show regions of equipotential.

Question Image

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

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Physics>Electricity and Magnetism>Electrostatics>Electrical Potential Energy

An electric dipole of dipole moment

\vec{P}

is placed parallel to the uniform electric field of intensity

\vec{E} .

On rotating it through

180 °,

the amount of work done is _______.

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrical Potential Energy

A system of three charges are placed as shown in the figure:
Question Image

D > > d,

the potential energy of the system is best given by:

HARD

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

A charged particle of mass

m

and charge

q

moving under the influence of uniform electric field

\vec{E} \hat{i}

and a uniform magnetic field

\vec{B} \hat{k}

follows a trajectory from point

P

Q

as shown in figure. The velocities at

P

and

Q

are respectively,

v \vec{i}

and

- 2 v \vec{j}

. Then which of the following statements (A, B, C, D) are the correct? (Trajectory shown is schematic and not to scale)

Question Image

(A)

E = \frac{3}{4} (\frac{m v^{2}}{q a})

(B)

Rate of work done by the electric field at P is

\frac{3}{4} (\frac{m v^{3}}{a})

(C)

Rate of work done by both the fields at Q is zero

(D)

The difference between the magnitude of angular momentum of the particle at P and Q is

2 m a v

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrical Potential Energy

A point charge

q

is rotated along a circle in the electric field generated by another point charge

Q

. The work done by the electric field on the rotating charge in one complete revolution is

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrical Potential Energy

A two point charges $4 q$ and $- q$ are fixed on the $x$ -axis at $x = \frac{- d}{2}$ and $x = \frac{d}{2}$ , respectively. If the third point charge ‘ $q$ ’ is taken from the origin to $x = d$ along the semicircle as shown in the figure, the energy of the charge will:

Question Image

EASY

Physics>Electricity and Magnetism>Electrostatics>Electrical Potential Energy

Derive an expression for the torque experienced by an electric dipole kept in a uniform electric field.

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrical Potential Energy

An electric dipole of dipole moment

\vec{p}

is placed in a uniform electric field of strength

\vec{E}

. If

θ

is the angle between the positive direction of

\vec{p}

and

\vec{E}

, then potential energy of the dipole is largest when

θ

HARD

Physics>Electricity and Magnetism>Electrostatics>Electrical Potential Energy

A point charge

- q

is carried from a point

A

to another point

B

on the axis of a charged ring of radius

r

carrying a charge

+ q .

If the point

A

is at a distance

\frac{4}{3} r

from the centre of the ring and the point

B

\frac{3}{4} r

from the centre but on the opposite side, what is the net work that need to be done for this?

Consider a metallic sphere of radius R concentric with another hollow metallic sphere of inner radius 2R and outer radius 3R as shown in the figure. The inner,sphere is given a charge -Q and outer +2Q. The electrostatic potential energy of the system is

Important Questions on Electrostatics

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Consider a metallic sphere of radius $R$ concentric with another hollow metallic sphere of inner radius $2 R$ and outer radius $3 R$ as shown in the figure. The inner,sphere is given a charge $- Q$ and outer $+ 2 Q$ . The electrostatic potential energy of the system is