EASY

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The electrostatic potential due to a short electric dipole at a distance $r$ varies as:

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Important Questions on Electrostatics

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)

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.

MEDIUM

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

Define electric potential. Obtain an expression of electric potential due to an electric dipole at any point

(r, θ)

. Draw necessary diagram.

HARD

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

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>Electrostatics>Potential Due to a Electric Dipole

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

EASY

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

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

HARD

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

Derive an expression for the electric potential at any point at a distance $r$ from the centre of an electric dipole. Hence find the potential if the point lies on

(i) axial line and (ii) equatorial line

EASY

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

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

EASY

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

The electric field and the potential of an electric dipole vary with distance

r

HARD

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

An electric dipole is formed by two charges $+ q$ and $- q$ located in $x y$ -plane at $(0, 2) mm$ and $(0, - 2) mm$ , respectively, as shown in the figure. The electric potential at point $P (100, 100) mm$ due to the dipole is $V_{0}$ . The charges $+ q$ and $- q$ are then moved to the points $(- 1, 2) mm$ and $(1, - 2) mm$ , respectively. What is the value of electric potential at $P$ due to the new dipole?

Question Image

MEDIUM

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

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>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

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

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:

EASY

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

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

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 :

HARD

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

Derive an expression for the electric potential at any point along the axial line of an 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

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:

The electrostatic potential due to a short electric dipole at a distance r varies as:

Important Questions on Electrostatics

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The electrostatic potential due to a short electric dipole at a distance $r$ varies as: