A uniformly charged solid sphere of radius R has potential V 0 (measured with respect to ∞ ) on its surface. For this sphere the equipotential surfaces with potential 3 V 0 2 , 5 V 0 4 , 3 V 0 4 and V 0 4 have radius R 1 , R 2 , R 3 and R 4 respectively. Then Note : This question had two option correct at the time of examination. Proper corrections are made in the question to avoid it.

R 1 ≠ 0 and R 2 - R 1 > ( R 4 - R 3 )

EASY

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Electric field in a region is increasing in magnitude along $x$ -direction. The equipotential surfaces associated are

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Important Questions on Electrostatics

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

Which statement(s) among the following are incorrect:
(i) A negative test charge experiences a force opposite to the direction of the field.
(ii) The tangent drawn to a line of force represents the direction of electric field.
(iii) The electric field lines never intersect.
(iv) The electric field lines form a closed loop.

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

The electric field lines on the left have twice the separation on those on the right as shown in figure. If the magnitude of the field at $A$ is $40 {Vm}^{- 1}$ , what is the force on $20 μ C$ charge kept at

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EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

Which is the INCORRECT statement regarding electric lines of force

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

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:

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

The angle between the electric lines of force and the equipotential surface is

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

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:

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

Figure shows three arrangements of electric field lines. In each arrangement, a proton is released from rest at point A and then accelerated through point B by the electric field. Points A and B have equal separations in the three arrangements. If $p_{1}, p_{2}$ and $p_{3}$ are linear momentum of the proton at point B in the three arrangement respectively, then

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EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

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>Electric Field Lines and Equipotential Surfaces

A long cylindrical shell carries positive surface charge

σ

in the upper half and negative surface charge

- σ

in the lower half. The electric field lines around the cylinder will look like figure given in:

(figures are schematic and not drawn to scale)

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

A point charge

+ Q

is placed just outside an imaginary hemispherical surface of radius R as shown in the figure. Which of the following statements is/are correct?

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MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

Two point charges

q_{1} (\sqrt{10} μC)

and

q_{2} (- 25 μC)

are placed on the

x

-axis at

x = 1 m

and

x = 4 m

respectively. The electric field

(in V m^{- 1})

at a point

y = 3 m

y

-axis is,

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

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

The work done to move a charge on an equipotential surface is

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

An infinitely long thin non-conducting wire is parallel to the z - axis and carries a uniform line charge density

λ

. It pierces a thin non-conducting spherical shell of radius

R

in such a way that the arc

P Q

subtends an angle

120^{o}

at the centre

O

of the spherical shell, as shown in the figure. The permittivity of free space is

ϵ_{0}

. Which of the following statements is (are) true?
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HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

A uniformly charged solid sphere of radius R has potential $V_{0}$ (measured with respect to $\infty$ ) on its surface. For this sphere the equipotential surfaces with potential $\frac{3 V_{0}}{2}, \frac{5 V_{0}}{4}, \frac{3 V_{0}}{4}$ and $\frac{V_{0}}{4}$ have radius $R_{1}$ , $R_{2}, R_{3}$ and $R_{4}$ respectively. Then

Note : This question had two option correct at the time of examination. Proper corrections are made in the question to avoid it.

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

A particle, of mass

10^{- 3} kg

and charge

1.0 C

, is initially at rest. At time

t = 0

, the particle comes under the influence of an electric field

\vec{E} (t) = E_{0} \sin (ω t) \hat{i}

, where

E_{0} = 1.0 N C^{- 1}

and

ω = 10^{3} rad s^{- 1}

. Consider the effect of only the electrical force on the particle. Then the maximum speed, in

m s^{- 1}

, attained by the particle at subsequent times is ____________.

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

A thin disc of radius $b = 2 a$ has a concentric hole of radius $a$ in it (see figure). It carries uniform surface charge $σ$ on it. If the electric field on its axis at a height $h (h < < a)$ from its centre is given as $C h$ then the value of $C$ is

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

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 :

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MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass ? (Curves are drawn schematically and are not to scale)

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

What is the angle between maximum value of potential gradient and equipotential surface?

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field Lines and Equipotential Surfaces

Within a spherical charge distribution of charge density

ρ (r),

N equipotential surfaces of potential

V_{0}, V_{0} + ∆ V, V_{0} + 2 ∆ V, \dots V_{0} + N ∆ V (∆ V > 0),

are drawn and have increasing radii

r_{0}, r_{1}, r_{2}, \dots r_{N},

respectively. If the difference in the radii of the surfaces is constant for all values of

V_{0} a n d ∆ V

then :

Electric field in a region is increasing in magnitude along x-direction. The equipotential surfaces associated are

Important Questions on Electrostatics

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Electric field in a region is increasing in magnitude along $x$ -direction. The equipotential surfaces associated are