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One half of a semicircular ring of radius $R$ has charge $- Q$ while the other half has $+ Q$ . The ring is placed in xy plane where a uniform electric field exists $\vec{E} = E_{0} \hat{i}$

Find the work required to be done by external agent to rotate the ring about $z$ axis by $90 °$ in clockwise direction.

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Important Questions on Electrostatics

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

An electric dipole is formed by two equal and opposite charges

q

with separation

d

. The charges have same mass m. It is kept in a uniform electric field

E .

If it is slightly rotated from its equilibrium orientation, then its angular frequency

ω

is:

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

Two electric dipoles,

A,

B

with respective dipole moments

\vec{d_{A}} = - 4 q a \hat{i}

and

\vec{d_{B}} = - 2 q a \hat{i}

are placed on the

x

-axis with a separation

R,

as shown in the figure

Question Image

The distance from

A

at which both of them produce the same potential is:

HARD

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

An electric dipole has 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_{1} \hat{j}

it experiences a torque

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

. The angle

θ

is:

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

An electric dipole of moment

\vec{p} = (- \hat{i} - 3 \hat{j} + 2 \hat{k}) \times 10^{- 29} C m

at the origin

(0, 0, 0)

. The electric field due to this dipole at

\vec{r} = + \hat{i} + 3 \hat{j} + 5 \hat{k}

(note that

\vec{r} \cdot \vec{p} = 0

) is parallel to:

HARD

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

An electric dipole lies in an electric field

\vec{E} = 1000 \hat{i} N / C

in such a position that its dipole moment is

(12 \hat{i} + 5 \hat{j}) \times 10^{- 29} C - m .

It is rotated so that the dipole moment becomes

(- 12 \hat{i} + 5 \hat{j}) \times 10^{- 29} C - m .

The work done by the external agent is

EASY

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

Which of the following molecules is a polar molecule?

EASY

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

An electric dipole is placed at an angle of

30 °

with an electric field intensity

2 \times 10^{5} {N C}^{- 1}

. It experiences a torque equal to

4 N m

. The charge on the dipole, if the dipole length is

2 cm

, is

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

A short electric dipole has a dipole moment of

16 \times 10^{- 9} C m

. The electric potential due to the dipole at a point at a distance of

0.6 m

from the centre of the dipole, situated on a line making an angle of

60 °

with the dipole axis is:

(\frac{1}{4 π ε_{0}} = 9 \times 10^{9} N m^{2} C^{- 2})

EASY

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

A large metal plate has a surface charge density of

8.85 \times 10^{- 6} C m^{- 2}

. An electron having initial kinetic energy of

8 \times 10^{- 17} J

is moving towards the center of the plate. If the electron stops just before reaching the plate then the initial distance between the electron and the plate is [Take

ε_{0} = 8.85 \times 10^{- 12} C^{2} N m^{- 2}

]

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

Charges

- q

and

+ q

, located at

A

and

B

, respectively, constitute an electric dipole. Distance

A B = 2 a

O

is the mid point of the dipole and

O P

is perpendicular to

A B

. A charge

Q

is placed at

P

where

O P = y

and

y ≫ 2 a

. The charge

Q

experiences an electrostatic force

F

. If

Q

is now moved along the equatorial line to

P'

such that

O P' = (\frac{y}{3})

the force on

Q

will be close to

(\frac{y}{3} ≪ 2 a)

EASY

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

An electric dipole is kept in non-uniform electric field. It generally experiences

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

An electric dipole of dipole moment

\vec{P}

is placed parallel to the uniform electric field of intensity

\vec{E} .

On rotating it through

180 °,

the amount of work done is _______.

EASY

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

The work done in moving a point charge of

10 μC

through a distance of

3 cm

along the equatorial axis of an electric dipole is

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

A Point dipole

\vec{p} = - p_{0} \hat{x}

is kept at the origin. The potential and electric field due to this dipole on the

y - a x i s

at a distance

d

are, respectively: (Taken

V = 0

at infinity)

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

Two identical electric point dipoles have dipole have dipole moments

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

and

{\vec{p}}_{2} = - p \hat{i}

and are held on the

x

-axis at distance '

a

' from each other. When released, they move along the

x

-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is '

m

', their speed when they are infinitely far apart is :

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

An electric dipole is kept in a uniform electric field with its axis inclined at some angle to the electric field. It experiences

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

The electric field at a point on the equatorial plane at a distance r from the centre of a dipole having dipole moment

\vec{p}

is given by (

r > >

separation of two charges forming the dipole,

ϵ_{0}

- permittivity of free space)

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure:

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

An electric dipole of dipole moment

\vec{p}

is placed in a uniform electric field of strength

\vec{E}

. If

θ

is the angle between the positive direction of

\vec{p}

and

\vec{E}

, then potential energy of the dipole is largest when

θ

HARD

Physics>Electricity and Magnetism>Electrostatics>Potential Energy in an External Field

A point charge

- q

is carried from a point

A

to another point

B

on the axis of a charged ring of radius

r

carrying a charge

+ q .

If the point

A

is at a distance

\frac{4}{3} r

from the centre of the ring and the point

B

\frac{3}{4} r

from the centre but on the opposite side, what is the net work that need to be done for this?

One half of a semicircular ring of radius R has charge -Q while the other half has +Q. The ring is placed in xy plane where a uniform electric field exists E→=E0i^ Find the work required to be done by external agent to rotate the ring about z axis by 90° in clockwise direction.

Important Questions on Electrostatics

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