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 .

EASY

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The electric field in a certain region of space obeys $E_{y} \neq 0, E_{x} = E_{z} = 0$ and $\frac{\partial \vec{E}}{\partial x} \neq 0, \frac{\partial \vec{E}}{\partial y} = \frac{\partial \vec{E}}{\partial z} = 0$ . Then, net torque on an electric dipole parallel to the $x -$ axis in this field is

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Important Questions on Electric Charges and Fields

MEDIUM

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

In the figure the net torque acting on the dipole is

Question Image

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

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)

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

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:

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

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

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 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

EASY

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

Which of the following molecules is a polar molecule?

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:

MEDIUM

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

MEDIUM

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

EASY

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

An electric dipole is kept in non-uniform electric field. It generally experiences

MEDIUM

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

MEDIUM

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

The electric field in a certain region of space obeys Ey≠0, Ex=Ez=0 and ∂E→∂x≠0, ∂E→∂y=∂E→∂z=0. Then, net torque on an electric dipole parallel to the x-axis in this field is

Important Questions on Electric Charges and Fields

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