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Important Questions on Electrostatics

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field

A particle of mass

2 \times 10^{- 6} kg

with a charge

5 \times 10^{- 6} C

is hanging in air above a similarly charged conducting surface. The charge density of the surface is (Assume

ϵ_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} M^{- 2}

and

g = 10 m s^{- 2}

)

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field

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

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field

An infinitely long thin straight wire has uniform charge density of

\frac{1}{4} \times 10^{- 2} C m^{- 1}

. What is the magnitude of electric field at a distance

20 cm

from the axis of the wire?

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field

The bob of a pendulum of mass $m$ suspended by an inextensible string of length $L$ as shown in the figure carries a small charge $q$ . An infinite horizontal plane conductor with uniform surface charge density $σ$ is placed below it. What will be the time period of the pendulum for small amplitude oscillations?

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MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field

Charges Q, 2Q and 4Q are uniformly distributed in three dielectric solid spheres 1, 2 and 3 of radii R/2, R and 2R respectively, as shown in the figure. If magnitudes of the electric fields at point P at a distance R from the centre of spheres 1, 2 and 3 are

E_{1}, E_{2}

and

E_{3}

respectively, then

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HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field

Four positive point charges

+ q

are kept at the four corners of a square of side

l

. The net electric field at the midpoint of any one side of the square is

(

take

\frac{1}{4 π \in_{0}} = k

)

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field

A thin spherical insulating shell of radius

R

carries a uniformly distributed charge such that the potential at its surface is

V_{0}

. A hole with a small area

α 4 π R^{2} (α ≪ 1)

is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field

Two small charged spheres A and B have charges

10 μ C

and

40 μ C

respectively and are held at separation of

90 cm

from each other. At what distance from A, electric field intensity would be zero ?

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field

A wire of length

L = 20 c m

is bent into a semi-circular arc and the two equal halves of the arc are uniformly charged with charges

+ Q

and

- Q

as shown in the figure. The magnitude of the charge on each half is

|Q| = 10^{3} ε_{0}

, where

ε_{0}

is the permittivity of free the space. The net electric field at the centre

O

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field

Two parallel infinite line charges with linear charge densities

+ λ C m^{- 1}

and

- λ C m^{- 1}

are placed at a distance of

2 R

in free space. What is the electric field mid-way between the two-line charges?

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field

As shown in the figure, a point charge

q_{1} = + 1 \times 10^{- 6} C

is placed at the origin in

x y

-plane and another point charge

q_{2} = + 3 \times 10^{- 6} C

is placed at the coordinate

(10, 0) .

In that case, which of the following graph

(s)

shows most correctly the electric field vector in

E_{x}

x

-direction ?

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field

A total charge

q

is divide as

q_{1}

and

q_{2}

which are kept at two of the vertices of an equilateral triangle of side

a

. The magnitude of the electric field E at the third vertex of the triangle is to be depicted schematically as a function of

x = \frac{q_{1}}{q}

. Choose the correct figure.

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field

Two mutually perpendicular infinitely long straight conductors carrying uniformly distributed charges of linear densities $λ_{1}$ and $λ_{2}$ are positioned at a distance $r$ from each other.

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Force between the conductors depends on $r$ as

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field

Point charges $+ q$ and $- q$ are located at the vertices of a square with diagonals $2 l$ as shown in the figure. The magnitude of the electric field strength at a point, located symmetrically with respect to the vertices of the square at a distance $x$ from its center is

Question Image

EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field

A current of $10 A$ is passing through a long wire which has a semicircular loop of the radius $20 cm$ as shown in the figure. Magnetic field produced at the centre of the loop is:

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Electric Field

Find the electric field at point $P$ (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length $L$ carrying a charge $Q$ . The distance of the point $P$ from the centre of the rod is $a = \frac{\sqrt{3}}{2} L$

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EASY

Physics>Electricity and Magnetism>Electrostatics>Electric Field

A cube of side $a$ has point charges $+ Q$ located at each of its vertices except at the origin where the charge is $- Q .$ The electric field at the centre of cube is:

Question Image

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field

Consider a sphere of radius

R

which carries a uniform charge density

ρ

. If a sphere of radius

\frac{R}{2}

is carved out of it, as shown, the ratio

\frac{|\vec{E_{A}}|}{|\vec{E_{B}}|}

of magnitude of electric field

\vec{E_{A}}

and

\vec{E_{B}}

, respectively, at points

A

and

B

due to the remaining portion is:

Question Image

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field

The figures below depict two situations in which two infinitely long static line charges of constant positive line charge density

λ

are kept parallel to each other. In their resulting electric field, point charges

q

and

- q

are kept in equilibrium between them. The point charges are confined to move in the

x

direction only. If they are given a small displacement about their equilibrium positions, then the correct statements(s) is (are)

Question Image

HARD

Physics>Electricity and Magnetism>Electrostatics>Electric Field

Two non-conducting solid spheres of radii $R$ and $2 R$ , having uniform volume charge densities $ρ_{1}$ and $ρ_{2}$ , respectively, touch each other. The net electric field at a distance $2 R$ from the centre of the smaller sphere, along the line joining the centres of the spheres, is zero. The ratio $\frac{ρ_{1}}{ρ_{2}}$ can be

The graph showing the variation of electric field (E) with the distance (r) from the centre of a conducting spherical shell is -

Important Questions on Electrostatics

Learn and Prepare for any exam you want !

The graph showing the variation of electric field $(E)$ with the distance $(r)$ from the centre of a conducting spherical shell is -