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A small dipole of dipole moment $p$ is placed at a distance $2 R$ from the centre of a neutral conducting sphere of radius $R .$ The direction of dipole is towards the centre of the sphere. A tangent is drawn from the centre of dipole to the sphere which meets the sphere at point $A .$

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Important Questions on Electrostatics

EASY

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

On the axis and on the equator of an electric dipole for all points ______

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

The electric field at a point on the equatorial plane at a distance r from the centre of a dipole having dipole moment

\vec{p}

is given by (

r > >

separation of two charges forming the dipole,

ϵ_{0}

- permittivity of free space)

HARD

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

Derive an expression for the intensity of the electric field at a point on the equatorial plane of an electric dipole.

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

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

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

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>Electrostatics>Potential Due to a Electric Dipole

A

system has two charges

q_{A} = 2.5 \times 10^{- 7} C

and

q_{B} = - 2.5 \times 10^{- 7} C

located at points

A : (0, 0, - 15 cm)

and

B : (0, 0, + 15 cm),

respectively. What is the magnitude and direction of electric dipole moment of the system?

HARD

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

Derive an expression for the intensity of the electric field at a point on the axial line of an electric dipole.

HARD

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

Obtain an expression for electric potential

' V'

at a point in an end

‐

on position i.e. axial position of an electric dipole.

EASY

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

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

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

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>Electrostatics>Potential Due to a Electric Dipole

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:

HARD

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

An electric dipole with dipole moment

\frac{p_{0}}{\sqrt{2}} (\hat{i} + \hat{j})

is held fixed at the origin

O

in the presence of an uniform electric field of magnitude

E_{0} .

If the potential is constant on a circle of radius

R

centered at the origin as shown in figure, then the correct statement(s) is/are:
(

ε_{0}

is permittivity of free space,

R ≫

dipole size)

Question Image

EASY

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

A dipole is placed in an electric field as shown. In which direction will it move?

Question Image

HARD

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

Two ideal electric dipoles $A$ and $B$ , having their dipole moment $p_{1}$ and $p_{2}$ respectively are placed on a plane with their centres at $O$ as shown in the figure. At point $C$ on the axis of dipole $A$ , the resultant electric field is making an angle of $37 °$ with the axis. The ratio of the dipole moment of $A$ and $B, \frac{p_{1}}{p_{2}}$ is $: ($ take $\sin 37 ° = \frac{3}{5})$

Question Image

EASY

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

Two charges $10 μC$ and $- 10 μC$ are placed at points A and B separated by a distance of $10 cm$ . Find the electric field at a point P on the perpendicular bisector of AB, at a distance of $12 cm$ from its mid-point.

Question Image

EASY

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

Define:

$(a)$ Electric dipole moment.

EASY

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

An electric dipole of dipole moment

4 \times 10^{- 9} C - m

is inclined at an angle

30^{o}

to a uniform electric field of magnitude

5 \times 10^{4} \frac{N}{C}

. Calculate the torque applied on electric dipole.

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

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>Electrostatics>Potential Due to a Electric Dipole

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)

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Potential Due to a Electric Dipole

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)

A small dipole of dipole moment p is placed at a distance 2R from the centre of a neutral conducting sphere of radius R. The direction of dipole is towards the centre of the sphere. A tangent is drawn from the centre of dipole to the sphere which meets the sphere at point A.

Important Questions on Electrostatics

Learn and Prepare for any exam you want !

A small dipole of dipole moment $p$ is placed at a distance $2 R$ from the centre of a neutral conducting sphere of radius $R .$ The direction of dipole is towards the centre of the sphere. A tangent is drawn from the centre of dipole to the sphere which meets the sphere at point $A .$