A pair of charge + q and - q , separated by a small distance 2a ia place in a electric field E → , so that the line joining the charges makes an angle θ with E → . Write the expression for torque ς and ς → .

The force acting on + q charge and - q charge are F + → = + q · E → F - → = - q · E → The parallel component cancels out each other because of equal magnitude and opposite direction the perpendicular component adds each other F → = F + → sin θ + F - → sin θ F → = 2 q E → sin θ we know that, Torque = Product of Force and Distance ζ = F → × 2 a ς = 4 a q E → sin θ

A pair of charge + q and - q , separated by a small distance 2a ia place in a electric field E → , so that the line joining the charges makes an angle θ with E → . Write the expression for torque ς and ς → .

The force acting on + q charge and - q charge are F + → = + q · E → F - → = - q · E → The parallel component cancels out each other because of equal magnitude and opposite direction the perpendicular component adds each other F → = F + → sin θ + F - → sin θ F → = 2 q E → sin θ we know that, Torque = Product of Force and Distance ζ = F → × 2 a ς = 4 a q E → sin θ

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. .

MEDIUM

Earn 100

A pair of charge $+ q$ and $- q$ , separated by a small distance 2a ia place in a electric field $\vec{E}$ , so that the line joining the charges makes an angle $θ$ with $\vec{E}$ . Write the expression for torque $ς$ and $|\vec{ς}|$ .

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}

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 :

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 _______.

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

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

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:

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:

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

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

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

EASY

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

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

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 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

A pair of charge +q and -q, separated by a small distance 2a ia place in a electric field E→, so that the line joining the charges makes an angle θwith E→. Write the expression for torque ς and ς→.

Important Questions on Electric Charges and Fields

Learn and Prepare for any exam you want !

A pair of charge $+ q$ and $- q$ , separated by a small distance 2a ia place in a electric field $\vec{E}$ , so that the line joining the charges makes an angle $θ$ with $\vec{E}$ . Write the expression for torque $ς$ and $|\vec{ς}|$ .