A uniformly charged solid sphere of radius R has potential V 0 (measured with respect to ∞ ) on its surface. For this sphere the equipotential surfaces with potential 3 V 0 2 , 5 V 0 4 , 3 V 0 4 and V 0 4 have radius R 1 , R 2 , R 3 and R 4 respectively. Then Note : This question had two option correct at the time of examination. Proper corrections are made in the question to avoid it.

R 1 ≠ 0 and R 2 - R 1 > ( R 4 - R 3 )

MEDIUM

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In the given diagram, there is a conducting sphere of radius $r_{1}$ which is surrounded by a dielectric of relative permittivity $ε_{r}$ . If conducting sphere is given charge $q$ , then the surface density of polarization charges, on the outer surface of the dielectric layer, is

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Important Questions on Electrostatics

EASY

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

There is a uniform spherically symmetric surface charge density at a distance

R_{0}

from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed

V (R (t))

of the distribution as a function of its instantaneous radius

R (t)

is:

HARD

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

A uniformly charged solid sphere of radius R has potential $V_{0}$ (measured with respect to $\infty$ ) on its surface. For this sphere the equipotential surfaces with potential $\frac{3 V_{0}}{2}, \frac{5 V_{0}}{4}, \frac{3 V_{0}}{4}$ and $\frac{V_{0}}{4}$ have radius $R_{1}$ , $R_{2}, R_{3}$ and $R_{4}$ respectively. Then

Note : This question had two option correct at the time of examination. Proper corrections are made in the question to avoid it.

EASY

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

An electron is moving around an infinite linear charge in circular path of diameter

0.30 m

. If linear charge density is

10^{6} \frac{C}{m}

, then calculate the speed of an electron.

(m_{c} = 9.0 \times 10^{- 31} kg, e = 1.6 \times 10^{- 19} C)

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

Three point charges

4 q, Q

and

q

are placed in a straight line of length

L

at points

0, \frac{L}{2}

and

L

respectively. The net force on charge

q

is zero. The value of

Q

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

A non-uniformly charged sphere has charge density given by

ρ = \frac{a r^{2}}{R}

where

a

is a constant,

r

is the distance from the centre and

R

is the radius of the sphere. Then the total charge inside the sphere is proportional to

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

A charge

Q

is uniformly distributed on the circumference of a circular ring of radius

a

. Find the intensity of the electric field at a point at a distance

x

from the centre of the axis of the ring.

EASY

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

What is volume charge density? Write its SI unit.

EASY

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

Four point charges $q_{A} = 2 μ C, q_{B} = - 5 μ C, q_{C} = 2 μ C, q_{D} = - 5 μ C$ are located at the corners of a square $A B C D$ of side $10 cm .$ The force acting on a charge of $1 μ C$ placed at centre of the square is

Question Image

EASY

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

Find out the surface charge density at the intersection of point

x = 3 m

plane and

x

-axis, in the region of uniform line charge of

8 nC m^{- 1}

lying along the

z

-axis in free space.

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

Sixty four conducting drops each of radius

0.02 m

and each carrying a charge of

5 μ C

are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

Three concentric metal shells

A, B

and

C

of respective radii

a, b

and

c (a < b < c)

have surface charge densities

+ σ, - σ

and

+ σ

respectively. The potential of shell

B

is:

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

Shown in the figure is a shell made of a conductor. It has inner radius $a$ and outer radius $b$ , and carries charge $Q$ . At its centre a dipole $\vec{p}$ is placed as shown then:
Question Image

HARD

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

Let

E_{1} (r), E_{2} (r)

and

E_{3} (r)

be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density

λ

, and an infinite plane with uniform surface charge density

σ

. If

E_{1} (r_{0}) = E_{2} (r_{0}) = E_{3} (r_{0})

at a given distance

r_{0}

, then

EASY

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

Define surface charge density and volume charge density of an electric charge. Also, state its unit.

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

Three charges are placed at the three vertices of an equilateral triangle of side $a$ as shown in the figure. The force experienced by the charge placed at the vertex $A$ in a direction normal to $B C$ is

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

Four equal charges of value

+ Q

are placed at any four vertices of a regular hexagon of side

a

. By suitably choosing the vertices, what can be the maximum possible magnitude of electric field at the centre of the hexagon?

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

Eleven equal point charges, all of them having a charge $+ Q,$ are placed at all the hour positions of a circular clock of radius $r$ except at the $10 h$ position. What is the electric field strength at the centre of the clock?

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

Charge is distributed within a sphere of radius

R

with a volume charge density

ρ (r) = \frac{A}{r^{2}} e^{- \frac{2 r}{a}},

where

A

and

a

are constants. If

Q

is the total charge of this charge distribution, the radius

R

is_____.

HARD

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

Two infinite planes each with uniform surface charge density

+ σ

are kept in such a way that the angle between them is

30^{o}

. The electric field in the region shown between them is given by:
Question Image

HARD

Physics>Electricity and Magnetism>Electrostatics>Continuous Charge Distribution

Let a total charge

2 Q

be distributed in a sphere of radius

R,

with the charge density given by

ρ (r) = k r,

where

r

is the distance from the centre. Two charges

A

and

B

, of

- Q

each, are placed on diametrically opposite points, at equal distance, a, from the centre. If

A

and

B

do not experience any force, then:

In the given diagram, there is a conducting sphere of radius r1 which is surrounded by a dielectric of relative permittivity εr. If conducting sphere is given charge q, then the surface density of polarization charges, on the outer surface of the dielectric layer, is

Important Questions on Electrostatics

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In the given diagram, there is a conducting sphere of radius $r_{1}$ which is surrounded by a dielectric of relative permittivity $ε_{r}$ . If conducting sphere is given charge $q$ , then the surface density of polarization charges, on the outer surface of the dielectric layer, is