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 )

HARD

Earn 100

Explain the superposition principle of forces for a charge. Does electric field obey superposition principle?

Important Questions on Electric Charges and Fields

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Superposition Principle

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>Electric Charges and Fields>Superposition Principle

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>Electric Charges and Fields>Superposition Principle

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

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Superposition Principle

Four charges each equal to

(- Q)

are placed at the four corners of a square and a charge

q

is placed at its centre. If the system of charges is in equilibrium, the value of

q

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Superposition Principle

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

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Superposition Principle

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?

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Superposition Principle

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

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MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Superposition Principle

For which of the following, the superposition principle does not hold?

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Superposition Principle

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:

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Superposition Principle

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>Electric Charges and Fields>Superposition Principle

Two electrons each are fixed at a distance

2 d .

A third charge proton placed at the midpoint is displaced slightly by a distance

x (x ≪ d)

perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency:
(

m =

mass of charged particle)

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Superposition Principle

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>Electric Charges and Fields>Superposition Principle

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>Electric Charges and Fields>Superposition Principle

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

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Superposition Principle

An infinite number of point charges, each carrying $1 μ C$ charge, are placed along the y-axis at $y = 1 m, 2 m, 4 m, 8 m . . . .$

The total force on a $1 C$ point charge, placed at the origin, is $x \times 10^{3} N$ . The value of $x$ , to the nearest integer, is ___ .

[Take $\frac{1}{4 π ϵ_{0}} = 9 \times 10^{9} N m^{2} C^{- 2}$ ]

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Superposition Principle

What will be the magnitude of the electric field at point $O$ as shown in the figure? Each side of the figure is $l$ and perpendicular to the other?

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Superposition Principle

The distance between two charges

q_{1} = + 2 μ C

and

q_{2} = + 8 μ C

15 cm .

Calculate the distance from the charge

q_{1}

to the points on the line segment joining the two charges where the electric field is zero.

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Superposition Principle

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

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Superposition Principle

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:

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Superposition Principle

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:

Explain the superposition principle of forces for a charge. Does electric field obey superposition principle?

Important Questions on Electric Charges and Fields

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