The diagrams below show regions of equipotential. A positive charge is moved from A to B in each diagram.

In all the four cases the work done is the same.

Maximum work is required to move q in figure (c).

Minimum work is required to move q in figure (a).

Maximum work is required to move q in figure (b).

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Electric potential due to point charge in air is expressed as $V = \frac{1}{4 {πε}_{0}} \cdot \frac{q}{r}$ as $V \propto \frac{1}{r}$ . i.e for $r = 0$ to $r = \infty$ potential varies

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Important Questions on Electrostatics

EASY

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

A metallic sphere is kept in between two oppositely charged plates. The most appropriate representation of the field lines is

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is :

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

Consider a cube of uniform charge density,

ρ

. The ratio of the electrostatic potential at the center of the cube to that at one of the corners of the cube is,

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at

P

, in the region, is found to vary between the limits

589.0 V

589.8 V

. What is the potential at a point on the sphere whose radius vector makes an angle of

60 °

with the direction of the field?

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

When an

α

-particle of mass

m

moving with a undefined velocity bombards on a heavy nucleus of charge

Ze

, its distance of the closest approach from the nucleus depends on

m

as:

EASY

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

An electron with an initial speed of

4 .0 \times 10^{6} m s^{- 1}

is brought to rest by an electric field. The mass and charge of an electron are

9 \times 10^{- 31} kg

and

1.6 \times 10^{- 19} C

, respectively. Identify the correct statement.

EASY

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

An electric field

\vec{E} = (25 \hat{i} + 30 \hat{j}) N C^{- 1}

exists in a region of space. If the potential at the origin is taken to be zero then the potential at

x = 2 m

y = 2 m

is:

HARD

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

Some equipotential surfaces are shown. The electric field at any point is

Question Image

HARD

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

Four equal point charges

Q

each are placed in the

x y

plane at

(0, 2), (4, 2), (4, - 2)

and

(0, - 2)

. The work required to put a fifth charge

Q

at the origin of the coordinate system will be:

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

A charge

Q

is distributed over three concentric spherical shells of radii

a, b, c (a < b < c)

such that their surface charge densities are equal to one another.

The total potential at a point at distance

r

from their common centre, where

r < a,

would be:

HARD

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

A point particle of mass $0.5 kg$ is moving along the $X$ -axis under a force described by the potential energy $V$ shown below. It is projected towards the right from the origin with a speed $v$ .

Question Image

What is the minimum value of $v$ for which the particle will escape infinitely far away from the origin?

HARD

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

Consider a spherical shell of radius

R

with a total charge

+ Q

uniformly spread on its surface (center of the shell lies at the origin

x = 0

). Two point charge,

+ q a n d - q

are brought, one after the other, from far away and placed at

x = - \frac{a}{2} a n d x = + \frac{a}{2} (a < R),

respectively. Magnitude of the work done in this process is

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

A certain p-n junction having a depletion region of width

20 μm,

was found to have a breakdown voltage of

100 V

. If the width of the depletion region is reduced to

1 μm

during its production, then it can be used as a zener diode for voltage regulation of:

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

Two equal charges of magnitude

Q

each are placed at a distance

d

apart. Their electrostatic energy is

E . A .

third charge

- \frac{Q}{2}

is brought midway between these two charges. The electrostatic energy of the system is now?

EASY

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

The diagrams below show regions of equipotential.

Question Image

A positive charge is moved from $A$ to $B$ in each diagram.

EASY

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

Assume that an electric field

\vec{E} = 30 x^{2} \hat{i}

exists in space. Then the potential difference

V_{A} - V_{O}

, where V_O is the potential at the origin and V_A the potential at x = 2 m is :

EASY

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

The electric potential at a point

(x, y)

in the

x

y

plane is given by

V = - K x y

The electric field intensity at a distance

r

from the origin varies as

EASY

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

If potential(in

volts

) in a region is expressed as

V (x, y, z) = 6 x y - y + 2 y z

, the electric field(in

N C^{- 1}

) at point

(1, 1, 0)

EASY

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

The maximum potential energy due to electrostatic repulsion between two hydrogen nucleus is nearly (radius of the nucleus

= 1.1

Fermi)

[\frac{1}{4 π ε_{0}} = 9 \times 10^{9} N m^{2} C^{- 2}]

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electrostatic Potential and Electrostatic Potential Energy

An infinite line of charge with uniform line charge density of

1 C m^{- 1}

is placed along the

y

-axis. A charge of

1 C

is placed on the

x

-axis at a distance of

d = 3 m

from the origin. At what distance

(r)

from the origin on the

x

-axis, the total electric field is zero.

N

(Assume

0 < r < d

)

Electric potential due to point charge in air is expressed as V=14πε0·qr as V∝1r. i.e for r=0 to r=∞ potential varies

Important Questions on Electrostatics

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Electric potential due to point charge in air is expressed as $V = \frac{1}{4 {πε}_{0}} \cdot \frac{q}{r}$ as $V \propto \frac{1}{r}$ . i.e for $r = 0$ to $r = \infty$ potential varies