EASY

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The electric potential due to an infinite uniformly charge of linear charge density $λ$ at a distance $r$ from it is given by $r_{o}$ is the reference point.

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Important Questions on Gauss's law and Its Application

HARD

Physics>Electricity and Magnetism>Gauss's law and Its Application>Calculation of Electric Potential

10^{6}

conducting droplets of radius

10^{- 6} m

each and each having an electrical charge of

2 \times 10^{- 14} C,

are merged together to form a single drop. If the droplets were initially far apart, how much work is done in assembling the single drop?

HARD

Physics>Electricity and Magnetism>Gauss's law and Its Application>Calculation of Electric Potential

A uniformly charged ring of radius

3 a

and total charge

q

is placed in

x ‐ y

plane centred at origin. A point charge

q

is moving towards the ring along the

z -

axis and has speed

v

z = 4 a

. The minimum value of

v

such that it crosses the origin is:

HARD

Physics>Electricity and Magnetism>Gauss's law and Its Application>Calculation of Electric Potential

A charge

+ q

is distributed over a thin ring of radius

r

with line charge density

λ = \frac{q \sin^{2} θ}{π r}

. Note that the ring is in the

X Y

-plane and

θ

is the angle made by

r

with the

X

-axis. The work done by the electric force in displacing a point charge

+ Q

from the centre of the ring to infinity is

HARD

Physics>Electricity and Magnetism>Gauss's law and Its Application>Calculation of Electric Potential

27

similar drops of mercury are maintained at

10 V

each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is ___________ times that of a smaller drop.

MEDIUM

Physics>Electricity and Magnetism>Gauss's law and Its Application>Calculation of Electric Potential

Two equal point charges are fixed at

x = - a

and

x = + a

on the

x

-axis. Another point charge

Q

is placed at the origin. The change in the electrical potential energy of

Q

, when it is displaced by a small distance

x

along the

x

-axis, is approximately proportional to

MEDIUM

Physics>Electricity and Magnetism>Gauss's law and Its Application>Calculation of Electric Potential

A charge

Q

is given to a spherical shell of radius

R

. The work done to distribute the charge

Q

on the surface of the sphere is

HARD

Physics>Electricity and Magnetism>Gauss's law and Its Application>Calculation of Electric Potential

Calculate the minimum value of

v

, with which

q

should be projected so that, it just reaches the centre of the ring.

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HARD

Physics>Electricity and Magnetism>Gauss's law and Its Application>Calculation of Electric Potential

A small positively charged ball of mass

m

is suspended by an insulating thread of negligible mass. Another positively charged small ball is moved very slowly from a large distance, until it is in the original position of the first ball. As a result, the first ball rises by

h

. How much work has been done?

EASY

Physics>Electricity and Magnetism>Gauss's law and Its Application>Calculation of Electric Potential

On moving a charge of

20 Coulomb

2 cm, 2 J

of work is done, then the potential difference between the points is

HARD

Physics>Electricity and Magnetism>Gauss's law and Its Application>Calculation of Electric Potential

A metal sphere of radius

0.1 m

was insulated from its surroundings and given a large positive charge. A small charge was brought from a distance point to a point

0.5 m

from the sphere's centre. The work done against the electric field was

W

and the force on the small charge at its final position was

F

. If the small charge has been moved to only

1 m

from the centre of the sphere, what would have been the values for the work done and the force?

MEDIUM

Physics>Electricity and Magnetism>Gauss's law and Its Application>Calculation of Electric Potential

Charges

+ q & - q

are placed at points

A & B

respectively which are a distance

2 L

apart,

C

is the mid-point between

A & B

. The work done in moving a charge

Q

along the semicircle

C R D

EASY

Physics>Electricity and Magnetism>Gauss's law and Its Application>Calculation of Electric Potential

Three charges $Q_{0}, - q$ and $- q$ are placed at the vertices of an isosceles right angle triangle as in the figure. The net electrostatic potential energy is zero if $Q_{0}$ is equal to

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