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

MEDIUM

Earn 100

Three small conducting spheres each of radius $a$ and charge $q$ is placed at the corners of an equilateral triangle of side length $l$ . The side length $l$ is considerably large than the dimensions of the spheres. Find the electrical potential energy of the system.

50% studentsanswered this correctly

Important Questions on Electrostatic Potential and Capacitance

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential Energy of a System of Charges

The work done to assemble the three charges in a configuration as shown in the figure below is

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential Energy of a System of Charges

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>Electrostatic Potential and Capacitance>Potential Energy of a System of Charges

The kinetic energy of an electron which is accelerated through a potential difference of

100 V

will be ___ .

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential Energy of a System of Charges

The charges

- q

+ Q

and

- q

are placed at equal distances along a straight line. If the total P.E. of the system is zero, the ratio

\frac{Q}{q}

becomes,

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential Energy of a 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 Energy of a System of Charges

Four identical point masses, each of mass

m

and carrying charge

+ q

are placed at the corners of a square of sides

a

on a frictionless plane surface. If the particles are released simultaneously, the kinetic energy of the system when they are infinitely far apart is

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential Energy of a System of Charges

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

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential Energy of a System of Charges

Consider a sphere of radius

R

with uniform charged density and total charge

Q .

The electrostatic potential distribution inside the sphere is given by

ϕ (r) = \frac{Q}{4 π ε_{0} R} [a + b {(\frac{r}{R})}^{c}] .

Note that the zero of potential is at infinity. The values of

(a, b, c)

are:

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential Energy of a System of Charges

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>Electrostatic Potential and Capacitance>Potential Energy of a System of Charges

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

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential Energy of a 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 Energy of a 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?

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential Energy of a System of Charges

A particle

A

has charge

+ q

and particle

B

has charge

+ 4 q

each of them having the same mass

m

. When allowed to fall from rest through the same electrical potential difference, the ratio of their speeds will become

MEDIUM

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential Energy of a System of Charges

Three point charges of

2 mC

each are kept at the vertices of an equilateral triangle of side

50 cm .

If the system is supplied energy at the rate of

2 kW,

the time taken to move one of the charges to the mid point of the line joining the other two charges is

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential Energy of a System of Charges

A proton and an antiproton come close to each other in vacuum such that the distance between them is

10 cm .

Consider the potential energy to be zero at infinity. The velocity at this distance will be:

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential Energy of a System of Charges

What is the ratio of their final velocity when an alpha particle and a proton are accelerated at the same potential difference from the rest?

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential Energy of a System of Charges

Consider a system of

N

electrons. Upon exchange of a pair of electrons, the Coulomb potential of the system

EASY

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential Energy of a System of Charges

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,

HARD

Physics>Electricity and Magnetism>Electrostatic Potential and Capacitance>Potential Energy of a 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 Energy of a 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:

Three small conducting spheres each of radius a and charge q is placed at the corners of an equilateral triangle of side length l. The side length l is considerably large than the dimensions of the spheres. Find the electrical potential energy of the system.

Important Questions on Electrostatic Potential and Capacitance

Learn and Prepare for any exam you want !

Three small conducting spheres each of radius $a$ and charge $q$ is placed at the corners of an equilateral triangle of side length $l$ . The side length $l$ is considerably large than the dimensions of the spheres. Find the electrical potential energy of the system.