A charge Q is distributed over three concentric spherical shells of radii a , b , c a < b < c such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a , would be:

Q a + b + c 4 π ϵ 0 a 2 + b 2 + c 2

Q a 2 + b 2 + c 2 4 π ϵ 0 a 3 + b 3 + c 3

Q 12 π ϵ 0 a b + b c + c a a b c

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A charge $Q$ is uniformly distributed over a long rod $A B$ of length $L$ as shown in the figure. The electric potential at the point $O$ lying at distance $L$ from the end $A$ is

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Important Questions on Electrostatics

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Alpha Question Bank for Medical: Physics>Chapter 22 - Electrostatics>Exercise-3>Q 34

Assume that an electric field $\vec{E} = 30 x^{2} \hat{i}$ exists in space. Then find the potential difference $V_{A} - V_{0},$ where $V_{0}$ is the potential at the origin and $V_{A}$ the potential at $x = 2 m$ is

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Alpha Question Bank for Medical: Physics>Chapter 22 - Electrostatics>Exercise-3>Q 35

A long cylindrical shell carries a positive surface charge

σ

in the upper half and a negative surface charge

- σ

in the lower half. The electric field lines around the cylinder will look like the figure given in: (figures are schematic and not drawn to scale)

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Alpha Question Bank for Medical: Physics>Chapter 22 - Electrostatics>Exercise-3>Q 36

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 potentials

\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

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Alpha Question Bank for Medical: Physics>Chapter 22 - Electrostatics>Exercise-3>Q 37

The region between two concentric spheres of radii $' a'$ and $' b',$ respectively (see figure), has volume charge density $ρ = \frac{A}{r},$ where $A$ is a constant and $r$ is the distance from the centre. At the centre of the spheres is a point charge $Q .$ The value of $A$ such that the electric field in the region between the spheres will be constant, is:

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Alpha Question Bank for Medical: Physics>Chapter 22 - Electrostatics>Exercise-3>Q 38

An electric dipole has a fixed dipole moment

\vec{p}

which makes angle

θ

with respect to

x

-axis. When subjected to an electric field

{\vec{E}}_{1} = E \hat{i}

, it experiences a torque

{\vec{T}}_{1} = τ \hat{k}

. When subjected to another electric field

{\vec{E}}_{2} = \sqrt{3} E \hat{j}

, it experiences torque

{\vec{T}}_{2} = - {\vec{T}}_{1}

. The angle

θ

is,

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Alpha Question Bank for Medical: Physics>Chapter 22 - Electrostatics>Exercise-3>Q 39

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

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Alpha Question Bank for Medical: Physics>Chapter 22 - Electrostatics>Exercise-3>Q 40

Three charges

+ Q, q, + Q

are placed respectively, at distance,

0, d / 2

and

d

from the origin, on the

x

-axis. If the net force experienced by

+ Q,

placed at

x = 0,

is zero, then value of

q

is:

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Alpha Question Bank for Medical: Physics>Chapter 22 - Electrostatics>Exercise-3>Q 41

For a uniformly charged ring of radius

R,

the electric field on its axis has the largest magnitude at a distance

h

from its centre. Then value of

h

A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at distance L from the end A is

Important Questions on Electrostatics

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A charge $Q$ is uniformly distributed over a long rod $A B$ of length $L$ as shown in the figure. The electric potential at the point $O$ lying at distance $L$ from the end $A$ is