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A system consists of uniformly charged sphere of radius $R$ and the surrounding medium is filled by a charge with volume density, $ρ = \frac{α}{r}$ , where $α$ is a positive constant and $r$ is the distance from the centre of sphere. The charge of the sphere, for which the electric field intensity $E$ , outside the sphere, is independent of $r$ , is

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Important Questions on Electrostatics

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

Two point charges

q_{1} (\sqrt{10} μC)

and

q_{2} (- 25 μC)

are placed on the

x

-axis at

x = 1 m

and

x = 4 m

respectively. The electric field

(in V m^{- 1})

at a point

y = 3 m

y

-axis is,

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

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii R/2, R and 2R respectively, as shown in the figure. If magnitudes of the electric fields at point P at a distance R from the centre of spheres 1, 2 and 3 are

E_{1}, E_{2}

and

E_{3}

respectively, then

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EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

The bob of a simple pendulum has mass

2 g

and a charge of

5.0 μ C .

It is at rest in a uniform horizontal electric field of intensity

2000 V / m

At equilibrium, the angle that the pendulum makes with the vertical is:

(t a k e g = 10 m / s^{2})

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

A particle of mass

m

and charge

q

is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed

v

on the distance

x

travelled by it is correctly given by (graphs are schematic and not drawn to scale)

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

The electric field in a certain region is acting radially outward and is given by

E = A r

. A charge contained in a sphere of radius

a

centred at the origin of the field will be given by

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

A simple pendulum of length

L

is placed between the plates of a parallel plate capacitor having electric field

E

, as shown in figure. Its bob has mass

m

and charge

q

. The time period of the pendulum is given by:
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MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

Two parallel infinite line charges with linear charge densities

+ λ C m^{- 1}

and

- λ C m^{- 1}

are placed at a distance of

2 R

in free space. What is the electric field mid-way between the two-line charges?

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

A particle of mass

m

and charge

q

is placed at rest in uniform electric field

E

and then released. The kinetic energy attained by the particle after moving a distance

y

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

A charged particle initially at rest at

O

, when released follows a trajectory as shown. Such a trajectory is possible in the presence of
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MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

A total charge

q

is divide as

q_{1}

and

q_{2}

which are kept at two of the vertices of an equilateral triangle of side

a

. The magnitude of the electric field E at the third vertex of the triangle is to be depicted schematically as a function of

x = \frac{q_{1}}{q}

. Choose the correct figure.

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

Three charged particles $A, B$ and $C$ with charges $- 4 q, 2 q$ and $- 2 q$ are present on the circumference of a circle of radius $d .$ The charged particles $A, C$ and centre $O$ of the circle formed an equilateral triangle as shown in the figure. The electric field at the point $O$ is
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HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

A particle, of mass

10^{- 3} kg

and charge

1.0 C

, is initially at rest. At time

t = 0

, the particle comes under the influence of an electric field

\vec{E} (t) = E_{0} \sin (ω t) \hat{i}

, where

E_{0} = 1.0 N C^{- 1}

and

ω = 10^{3} rad s^{- 1}

. Consider the effect of only the electrical force on the particle. Then the maximum speed, in

m s^{- 1}

, attained by the particle at subsequent times is ____________.

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

Consider a sphere of radius

R

which carries a uniform charge density

ρ

. If a sphere of radius

\frac{R}{2}

is carved out of it, as shown, the ratio

\frac{|\vec{E_{A}}|}{|\vec{E_{B}}|}

of magnitude of electric field

\vec{E_{A}}

and

\vec{E_{B}}

, respectively, at points

A

and

B

due to the remaining portion is:

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HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

Four point charges

- q, + q, + q

and

- q

are placed on y-axis at

y = - 2 d, y = - d,

and

y = + 2 d,

respectively. The magnitude of the electric field

E

at a point on the x-axis at

x = D,

with

D ≫ d,

will behave as:

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

A thin spherical insulating shell of radius

R

carries a uniformly distributed charge such that the potential at its surface is

V_{0}

. A hole with a small area

α 4 π R^{2} (α ≪ 1)

is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

A charged particle (mass $m$ and charge $q$ ) moves along $X$ axis with velocity $V_{0}$ . When it passes through the origin it enters a region having uniform electric field $\vec{E} = - E \hat{j}$ which extends upto $x = d$ . Equation of path of electron in the region $x > d$ is:

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EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

Two charged thin infinite plane sheets of uniform charge density

σ_{+}

and

σ_{-}

, where

|σ_{+}| > |σ_{-}|

, intersect at the right angle. Which of the following best represents the electric field lines for the system:

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

An electric field due to a positively charged long straight wire at a distance

r

from it is proportional to

r^{- 1}

in magnitude. Two electrons are orbiting such a long straight wire in circular orbits of radii

1 \overset{\circ}{A}

and

2 \overset{\circ}{A}

. The ratio of their respective time periods is

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

A wire of length

L = 20 c m

is bent into a semi-circular arc and the two equal halves of the arc are uniformly charged with charges

+ Q

and

- Q

as shown in the figure. The magnitude of the charge on each half is

|Q| = 10^{3} ε_{0}

, where

ε_{0}

is the permittivity of free the space. The net electric field at the centre

O

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field (Discrete and Continuous Charge Distributions)

A thin disc of radius $b = 2 a$ has a concentric hole of radius $a$ in it (see figure). It carries uniform surface charge $σ$ on it. If the electric field on its axis at a height $h (h < < a)$ from its centre is given as $C h$ then the value of $C$ is

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Important Questions on Electrostatics

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