EASY

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What is the center of charge?

Important Questions on Electric Charges and Fields

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Dipole

Let

E_{1} (r), E_{2} (r)

and

E_{3} (r)

be the respective electric fields at a distance r from a point charge Q, an infinitely long wire with constant linear charge density

λ

, and an infinite plane with uniform surface charge density

σ

. If

E_{1} (r_{0}) = E_{2} (r_{0}) = E_{3} (r_{0})

at a given distance

r_{0}

, then

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Dipole

Define surface charge density and volume charge density of an electric charge. Also, state its unit.

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Dipole

Sixty four conducting drops each of radius

0.02 m

and each carrying a charge of

5 μ C

are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>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)

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Dipole

A non-uniformly charged sphere has charge density given by

ρ = \frac{a r^{2}}{R}

where

a

is a constant,

r

is the distance from the centre and

R

is the radius of the sphere. Then the total charge inside the sphere is proportional to

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Dipole

Charge is distributed within a sphere of radius

R

with a volume charge density

ρ (r) = \frac{A}{r^{2}} e^{- \frac{2 r}{a}},

where

A

and

a

are constants. If

Q

is the total charge of this charge distribution, the radius

R

is_____.

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Dipole

A charge

Q

is uniformly distributed on the circumference of a circular ring of radius

a

. Find the intensity of the electric field at a point at a distance

x

from the centre of the axis of the ring.

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>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 :

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Dipole

Find out the surface charge density at the intersection of point

x = 3 m

plane and

x

-axis, in the region of uniform line charge of

8 nC m^{- 1}

lying along the

z

-axis in free space.

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Dipole

What is volume charge density? Write its SI unit.

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>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>Electric Charges and Fields>Electric Dipole

Shown in the figure is a shell made of a conductor. It has inner radius $a$ and outer radius $b$ , and carries charge $Q$ . At its centre a dipole $\vec{p}$ is placed as shown then:
Question Image

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>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)

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Dipole

There is a uniform spherically symmetric surface charge density at a distance

R_{0}

from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed

V (R (t))

of the distribution as a function of its instantaneous radius

R (t)

is:

MEDIUM

Physics>Electricity and Magnetism>Electric Charges and Fields>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:

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Dipole

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

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Dipole

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

EASY

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Dipole

An electron is moving around an infinite linear charge in circular path of diameter

0.30 m

. If linear charge density is

10^{6} \frac{C}{m}

, then calculate the speed of an electron.

(m_{c} = 9.0 \times 10^{- 31} kg, e = 1.6 \times 10^{- 19} C)

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Dipole

Two infinite planes each with uniform surface charge density

+ σ

are kept in such a way that the angle between them is

30^{o}

. The electric field in the region shown between them is given by:
Question Image

HARD

Physics>Electricity and Magnetism>Electric Charges and Fields>Electric Dipole

Let a total charge

2 Q

be distributed in a sphere of radius

R,

with the charge density given by

ρ (r) = k r,

where

r

is the distance from the centre. Two charges

A

and

B

, of

- Q

each, are placed on diametrically opposite points, at equal distance, a, from the centre. If

A

and

B

do not experience any force, then:

What is the center of charge?

Important Questions on Electric Charges and Fields

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