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If potential energy of a dipole is chosen to be zero when dipole moment vector makes angle $\frac{π}{3}$ with uniform electric field $E$ . Then potential energy when dipole moment vector becomes parallel to electric field will become

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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?

If potential energy of a dipole is chosen to be zero when dipole moment vector makes angle π3 with uniform electric field E. Then potential energy when dipole moment vector becomes parallel to electric field will become

Important Questions on Electrostatics

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If potential energy of a dipole is chosen to be zero when dipole moment vector makes angle $\frac{π}{3}$ with uniform electric field $E$ . Then potential energy when dipole moment vector becomes parallel to electric field will become