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A semi-circular arc of radius a is charged uniformly and the charge per unit length is $λ .$ the electric field at its centre is

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Important Questions on Electrostatics

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

A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field

\vec{E}

. Due to the force

q \vec{E}

, its velocity increases from 0 to

6 m s^{- 1}

in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between

0

3

seconds are respectively

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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)

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 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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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?

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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.

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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 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

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

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

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

is:

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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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})

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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)

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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

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:

Question Image

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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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}]

HARD

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

An electron falls from rest through a vertical distance

h

in a uniform and vertically upward directed electric field

E

. The direction of electric filed is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance

h

. The time of fall of the electron, in comparison to the time of fall of the proton is

A semi-circular arc of radius a is charged uniformly and the charge per unit length is λ. the electric field at its centre is

Important Questions on Electrostatics

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A semi-circular arc of radius a is charged uniformly and the charge per unit length is $λ .$ the electric field at its centre is