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

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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Work required to set up the four charge configuration into a square shape of side length $a$ (as shown in the figure) is

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Important Questions on Electrostatic Potential and Capacitance

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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

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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

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

Question Image

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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:

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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:

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

100 V

will be ___ .

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:

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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

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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,

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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:

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?

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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

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

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?

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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

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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

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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.

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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?

Work required to set up the four charge configuration into a square shape of side length a (as shown in the figure) is

Important Questions on Electrostatic Potential and Capacitance

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Work required to set up the four charge configuration into a square shape of side length $a$ (as shown in the figure) is