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 .

HARD

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A point charge $q$ of mass $m$ is suspended vertically by a string of length $ℓ .$ A point dipole of dipole moment $\vec{p}$ is now brought towards $q$ from infinity so that the charge moves away. The final equilibrium position of the system including the direction of the dipole, the angles and distances is shown in the figure below. If the work done in bringing the dipole to this position is $N \times (m g h),$ where $g$ is the acceleration due to gravity, then the value of $N$ is (Note that for three coplanar forces keeping a point mass in equilibrium, $\frac{F}{\sin θ}$ is the same for all forces, where $F$ is any one of the forces and $θ$ is the angle between the other two forces)

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Important Questions on Electric Charges and Fields

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform External Field

In the figure the net torque acting on the dipole is

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform External Field

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

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform 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}

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform 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

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform 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

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform External Field

An electric dipole having point charges $+ q$ and $- q$ , separated by a fixed distance $d$ is kept under the influence of a uniform electric field $E$ , such that the axis of the dipole is making an angle $θ = 45 °$ with the direction of $E$ , as shown in the figure. If the electric dipole is allowed to rotate in the $x y$ -plane with its center being stationary, what is the magnitude of the net torque acting on the electric dipole?

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform 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 _______.

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform External Field

An electric dipole having a dipole moment

\vec{p}

is initially aligned along a uniform electric field

\vec{E}

. If the dipole is rotated from its equilibrium position by a small angle, it would execute simple harmonic oscillation. If the moment of inertia of the dipole is

I

, the period of oscillation is

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform 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

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform 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

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform External Field

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

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform 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:

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform External Field

An electric dipole of length

10 cm

having charges

\pm 6 \times 10^{- 3} C

, placed at

30 °

with respect to a uniform electric field experiences a torque of magnitude

6 \sqrt{3} Nm

. The magnitude of the electric field is

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform 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 ?

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform 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>Electric Charges and Fields>Dipole in a Uniform External Field

An electric dipole consisting of charges

+ q

and

- q

separated by a distance

L

is in stable equilibrium in a uniform electric field

\vec{E}

.The electrostatic potential energy of the dipole is :

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform External Field

A dipole of charge

0.01 C

and separation

0.4 mm

, is placed in an electric field of strength

10 dyn C^{- 1}

. Find the maximum torque exerted on the dipole in the field

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform 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>Electric Charges and Fields>Dipole in a Uniform 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:

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Dipole in a Uniform 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

Important Questions on Electric Charges and Fields

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