HARD

Earn 100

In a conducting metallic sphere of radius $2 r$ , an spherical cavity of radius $r$ is made. A charge $q$ is kept at the centre of the cavity as shown in the figure. Find the magnitude of the total electric field at $(4 r, 0, 0) .$

100% studentsanswered this correctly

Important Questions on Electrostatics

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field

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:

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field

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

Question Image

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field

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})

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field

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}]

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field

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

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)

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field

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

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

A charged particle initially at rest at

O

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

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field

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

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
Question Image

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field

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

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:

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field

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:
Question Image

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field

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

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:

Question Image

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field

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

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

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field

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

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field

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

Question Image

In a conducting metallic sphere of radius 2r, an spherical cavity of radius r is made. A charge q is kept at the centre of the cavity as shown in the figure. Find the magnitude of the total electric field at 4r, 0, 0.

Important Questions on Electrostatics

Learn and Prepare for any exam you want !

In a conducting metallic sphere of radius $2 r$ , an spherical cavity of radius $r$ is made. A charge $q$ is kept at the centre of the cavity as shown in the figure. Find the magnitude of the total electric field at $(4 r, 0, 0) .$