A point dipole with dipole moment, p = p 0 K ^ , is kept at the origin. An external electric field given by E = E 0 2 i ^ - 3 j ^ + 4 k ^ , is applied on it. Which one of the following statement is true ?

The force on the dipole is zero while torque rotates the dipole on the x y -plane.

The force on the dipole moves it along the direction of electric field.

The interaction energy between the dipole and electric field is zero.

The potential due to the dipole alone on the x y -plane with z = 0 depends on the value of p 0 .

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What work must be done to rotate and electric dipole through an angle $θ$ with the electric field, if an electric dipole of moment p is placed in an uniform electric field E with p parallel to E?

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Important Questions on Electrostatics

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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

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

Write the expression for magnetic potential energy of a magnetic dipole kept in a uniform magnetic field and explain the terms.

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

An electric dipole of dipole moment is

6.0 \times 10^{- 6} C m

placed in a uniform electric field of

1.5 \times 10^{3} N C^{- 1}

in such a way that dipole moment is along electric field. The work done in rotating dipole by

180 °

in this field will be_______

mJ

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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

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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

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:

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

Define electric dipole moment. An electric dipole is placed within a uniform electric field $(E)$ and is rotated to an angle $θ = 180 °$ . Find out the work done.

MEDIUM

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

An electric dipole is formed with two point charges

+ 3.2 \times 10^{- 19} C

and

- 3.2 \times 10^{- 19} C

and separated by a distance of

2.4 \times 10^{- 10} m

. The work done in rotating the dipole through

180 °

from the position of equilibrium in a uniform electric field

4 \times 10^{5} {Vm}^{- 1}

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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

Derive an expression for potential energy of an electric dipole placed in a uniform electric field.

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

A dipole of dipole moment

' P'

and moment of inertia

I

is placed in a uniform electric field

\vec{E}

. If it is displaced slightly from its stable equilibrium position, the period of oscillation of dipole is

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 _______.

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

An electric dipole of length

5 cm

is placed in an uniform electric field of

5 \times 10^{5} N C^{- 1}

at an angle of

30 °

with the charges

+ 10 mC

and

- 10 mC

on the dipole. The dipole experiences a torque of

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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:

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

An electric dipole consists of two opposite charges, each of magnitude

1.0 μC

separated by a distance of

2.0 cm .

The dipole is placed in an external field of

10^{5} {NC}^{- 1}

The maximum torque on the dipole is

MEDIUM

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

A point dipole with dipole moment,

p = p_{0} \hat{K},

is kept at the origin. An external electric field given by

E = E_{0} (2 \hat{i} - 3 \hat{j} + 4 \hat{k}),

is applied on it. Which one of the following statement is true ?

EASY

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

In the figure the net torque acting on the dipole is

Question Image

EASY

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

Derive an expression for the torque experienced by an electric dipole kept in a uniform electric field.

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?

What work must be done to rotate and electric dipole through an angle θ with the electric field, if an electric dipole of moment p is placed in an uniform electric field E with p parallel to E?

Important Questions on Electrostatics

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What work must be done to rotate and electric dipole through an angle $θ$ with the electric field, if an electric dipole of moment p is placed in an uniform electric field E with p parallel to E?