The electric field E is measured at a point P ( 0 , 0 , d ) generated due to various charge distributions and the dependence of E on d is found to be different for different charge distributions. List-I contains different relations between E and d . List-II describes different electric charge distributions, along with their locations. Match the functions in List-I with the related charge distributions in List-II. List-I List-II P. E is independent of d 1. A point charge Q at the origin. Q. E ∝ 1 d 2. A small dipole with point charges Q at ( 0 , 0 , l ) and – Q at ( 0 , 0 , – l ) . Take 2 l ≪ d . R. E ∝ 1 d 2 3. An infinite line charge coincident with the x - axis, with uniform linear charge density λ . S. E ∝ 1 d 3 4. Two infinite wires carrying uniform linear charge density parallel to the x - axis. The one along ( y = 0 , z = l ) has a charge density + λ and the one along ( y = 0 , z = – l ) has a charge density - λ . Take 2 l ≪ d 5. Infinite plane charge coincident with the x y - plane with uniform surface charge density.

P → 5 ; Q → 3 ; R → 1 , 4 ; S → 2

P → 5 ; Q → 3 , 4 ; R → 1 ; S → 2

P → 5 ; Q → 3 ; R → 1 , 2 ; S → 4

P → 4 ; Q → 2 , 3 ; R → 1 ; S → 5

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Consider a uniform spherical charge distribution of radius $R_{1}$ centred at the origin $O$ . In this distribution, a spherical cavity of radius $R_{2}$ , centred at $P$ with distance $O P = a = R_{1} - R_{2}$ (see figure) is made. If the electric field inside the cavity at position $\overset{⇀}{r}$ is $\overset{⇀}{E} (\overset{⇀}{r})$ , then the correct statement(s) is(are)

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Important Questions on Electrostatics

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Alpha Question Bank for Engineering: Physics>Chapter 22 - Electrostatics>Exercise - 3>Q 29

A point charge $+ Q$ is placed just outside an imaginary hemispherical surface of radius $R$ as shown in the figure. Which of the following statements is/are correct?

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Alpha Question Bank for Engineering: Physics>Chapter 22 - Electrostatics>Exercise - 3>Q 30

An infinitely long thin non-conducting wire is parallel to the

z -

axis and carries a uniform line charge density

λ

. It pierces a thin non-conducting spherical shell of radius

R

in such a way that the arc

PQ

subtends an angle

120^{°}

at the centre O of the spherical shell, as shown in the figure. The permittivity of free space is

ε_{0}

. Which of the following statements is (are) true?

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Alpha Question Bank for Engineering: Physics>Chapter 22 - Electrostatics>Exercise - 3>Q 32

The electric field

E

is measured at a point

P (0, 0, d)

generated due to various charge distributions and the dependence of

E

d

is found to be different for different charge distributions. List-I contains different relations between

E

and

d

. List-II describes different electric charge distributions, along with their locations. Match the functions in List-I with the related charge distributions in List-II.

List-I	List-II
P. $E$ is independent of $d$	1. A point charge $Q$ at the origin.
Q. $E \propto \frac{1}{d}$	2. A small dipole with point charges $Q$ at $(0, 0, l)$ and $- Q at (0, 0, - l)$ . Take $2 l ≪ d$ .
R. $E \propto \frac{1}{d^{2}}$	3. An infinite line charge coincident with the $x -$ axis, with uniform linear charge density $λ$ .
S. $E \propto \frac{1}{d^{3}}$	4. Two infinite wires carrying uniform linear charge density parallel to the $x -$ axis. The one along $(y = 0, z = l)$ has a charge density $+ λ$ and the one along $(y = 0, z = - l)$ has a charge density $- λ$ . Take $2 l ≪ d$
	5. Infinite plane charge coincident with the $x y -$ plane with uniform surface charge density.

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Alpha Question Bank for Engineering: Physics>Chapter 22 - Electrostatics>Exercise - 3>Q 33

An electric charge

10^{- 3} μC

is placed at the origin

(0, 0)

X Y

coordinate system. Two points

A

and

B

are situated at

(\sqrt{2}, \sqrt{2})

and

(2, 0)

respectively. The potential difference between the points

A

and

B

will be

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

Charges are placed on the vertices of a square as shown. Let $E$ be the electric field and $V$ the potential at the centre. If the charges on $A$ and $B$ are interchanged with those on $D$ and $C$ , respectively, then

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

The potential at a point

x

(measured in

μm

) due to some charges situated on the

x

-axis is given by

V (x) = 20 / (x^{2} - 4) volts

. The electric field

E

x = 4 μm

is given by

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

A thin spherical shell of the radius

R

has a charge

Q

spread uniformly over its surface. Which of the following graphs most closely represents the electric field

E (r)

produced by the shell in the range

0 \leq r < \infty

, where

r

is the distance from the centre of the shell?

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

Two points

P

and

Q

are maintained at the potentials of

10 V

and

- 4 V

, respectively. The work done in moving

100

electrons from

P

Q

Important Questions on Electrostatics

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