A pair of charges + q and - q , separated by a small distance 2 a is placed in an electric field E → , so that the line joining the charges makes an angle θ with E → . Write the expressions for torque and also its magnitude.

When a pair of charges + q and - q are placed in an electric field E → such that the line joining the charges makes an angle θ with the direction of the electric field, the charges experience an electric force. This force tends to rotate the charges around their centre of mass, creating a torque. The formula to calculate the torque on + q is given by τ + = 2 q E a sin θ . . . 1 and the formula to calculate the torque on - q is given by τ - = - 2 q E a sin θ . . . 2 Hence, the total magnitude of torque on the system of charges can be written as τ → = τ + + τ - = 0

A pair of charges + q and - q , separated by a small distance 2 a is placed in an electric field E → , so that the line joining the charges makes an angle θ with E → . Write the expressions for torque and also its magnitude.

When a pair of charges + q and - q are placed in an electric field E → such that the line joining the charges makes an angle θ with the direction of the electric field, the charges experience an electric force. This force tends to rotate the charges around their centre of mass, creating a torque. The formula to calculate the torque on + q is given by τ + = 2 q E a sin θ . . . 1 and the formula to calculate the torque on - q is given by τ - = - 2 q E a sin θ . . . 2 Hence, the total magnitude of torque on the system of charges can be written as τ → = τ + + τ - = 0

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 .

There is an electric dipole in X-Y plane .Its dipole moment is 4 × 10 - 9 Cm On the same plane there is also a uniform electric field of magnitude 5 × 10 4 NC - 1 . If the axis of dipole makes an angle 30 ° with the electric field . Calculate the magnitude of torque acting on the dipole and also mention the direction of the torque

Given the electric dipole moment, p = 4 × 10 - 9 Cm . Angle made by p with a uniform electric field, θ = 30 ° . Electric field, E = 5 × 10 4 NC - 1 . The torque acting on the dipole, τ = pE sinθ = 4 × 10 - 9 × 5 × 10 4 sin 30 = 20 × 10 - 9 × 10 4 × 1 2 = 10 - 4 Nm . Hence, the torque is 10 - 4 Nm ., As the torque is the cross product of the field and the dipole moment, its direction is given by Fleming's right-hand rule. .

EASY

Earn 100

A pair of charges $+ q$ and $- q$ , separated by a small distance $2 a$ is placed in an electric field $\vec{E}$ , so that the line joining the charges makes an angle $θ$ with $\vec{E}$ . Write the expressions for torque and also its magnitude.

Important Questions on Electric Charges and Fields

MEDIUM

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

A dipole is placed in a uniform electric field with its axis parallel to the field. It experiences:

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 ?

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

An electric dipole with dipole moment $4 \times 10^{- 9} C m$ is inclined at $30 °$ with the direction of a uniform electric field of magnitude ${5×10}^{4} N C^{- 1}$ . Calculate the magnitude of torque acting on the dipole.

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

MEDIUM

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

Obtain an expression for the torque on an electric dipole placed in a uniform electric field.

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

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

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 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}

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 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>Electric Charges and Fields>Dipole in a Uniform External Field

Derive the expression for a couple acting on an electric dipole in a uniform electric field.

EASY

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

There is an electric dipole in X-Y plane .Its dipole moment is $4 \times 10^{- 9} Cm$ On the same plane there is also a uniform

electric field of magnitude $5 \times 10^{4} {NC}^{- 1}$ . If the axis of dipole makes an angle $30 °$ with the electric field . Calculate the magnitude of torque acting on the dipole and also mention the direction of the torque

MEDIUM

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

Derive an expression for the torque acting on an electric dipole placed at an angle

θ

with the direction of uniform electric field.

EASY

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

Two electric dipoles of dipole moments

1.2 \times 10^{- 30} cm

and

2.4 \times 10^{- 30} cm

are placed in two difference uniform electric fields of strengths

5 \times 10^{4} N C^{- 1}

and

15 \times 10^{4} N C^{- 1}

respectively. The ratio of maximum torque experienced by the electric dipoles will be

\frac{1}{x}

. The value of

x

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

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

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>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:

A pair of charges +q and - q, separated by a small distance 2a is placed in an electric field E→, so that the line joining the charges makes an angle θ with E→. Write the expressions for torque and also its magnitude.

Important Questions on Electric Charges and Fields

Learn and Prepare for any exam you want !

A pair of charges $+ q$ and $- q$ , separated by a small distance $2 a$ is placed in an electric field $\vec{E}$ , so that the line joining the charges makes an angle $θ$ with $\vec{E}$ . Write the expressions for torque and also its magnitude.