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A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of –3Q, the new potential difference between the same two surfaces is

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Important Questions on Electrostatics

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

A positive charge

q

is placed at the centre of a neutral hollow cylindrical conducting shell with its cross section as shown in the figure below.

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Which one of the following figures correctly indicates the induced charge distribution in the conductor (ignore edge effects).

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

Two long concentric hollow metallic cylinders of radii $a$ and $b$ , respectively carry equal and opposite charges $- σ$ and $+ σ$ per unit length, as shown. The space between the cylinders is filled with air. The distance measured from the central axis is denoted by $r .$

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Which of the following statements is NOT CORRECT?

EASY

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

Given below are two statements.
Statement I : Electric potential is constant within and at the surface of each conductor.

Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.

In the light of the above statements, choose the most appropriate answer from the options give below.

EASY

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

When a soap bubble is charged?

EASY

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

A hollow conducting sphere is placed in an electric field produced by a point charge placed at $P$ as shown in figure. Let $V_{A}, V_{B}, V_{C}$ be the potentials at points $A, B$ and $C$ , respectively. Then

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HARD

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

Write any five application of superconductors.

HARD

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

Two uniformly charged spherical conductors

A

and

B

of radii

5 mm

and

10 mm

are separated by a distance of

2 cm

. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere

A

and

B

will be

HARD

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

The potential (in volts) of a charge distribution is given by

V (z) = 30 - 5 z^{2}

for

|z| \leq 1 m

V (z) = 35 - 10 |z|

for

|z| \geq 1 m

V (z)

does not depend on x and y. If this potential is generated by a constant charge per unit volume

ρ_{0}

(in units of

ϵ_{0}

) which is spread over a certain region, then choose the correct statement.

EASY

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

A spherical conductor $A$ is placed concentrically inside a hollow spherical conductor $B$ . The charge $+ Q$ is given to $A$ and $B$ is earthed. Then the electric field is not zero

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EASY

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

Two charged spherical conductors of radius

R_{1}

and

R_{2}

are connected by a wire. Then the ratio of surface charge densities of the spheres

(σ_{1} / σ_{2})

is :

HARD

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

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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MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

The excess of pressure, due to surface tension, on a spherical liquid drop of radius

R

is proportional to

EASY

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

Shown in the figure are two point charges

+ Q

and

- Q

inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If

σ_{1}

is the surface charge on the inner surface and

Q_{1}

net charge on it and

σ_{2}

the surface charge on the outer surface and

Q_{2}

net charge on it then:

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MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

A metallic sphere is placed in a uniform electric field. The line of force follow the path(s) shown in the figure as,

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HARD

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density

ρ = \frac{A}{r}

, where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is:

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HARD

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

In finding the electric field using Gauss law the formula

|\vec{E}| = \frac{q_{e n c}}{ε_{0} |A|}

is applicable. In the formula

ε_{0}

is permittivity of free space,

A

is the area of Gaussian surface and

q_{e n c}

is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation?

HARD

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

A charged shell of radius

R

carries a total charge

Q .

Given

Φ

as the flux of electric field through a closed cylindrical surface of height

h,

radius

r

and with its center same as that of the shell. Here, center of the cylinder is a point on the axis of the cylinder which is equidistant from its top and bottom surfaces. Which of the following option(s) is/are correct? [

\in_{0}

is the permittivity of free space]

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

Conventionally which coloured wire is used for earthing?

HARD

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

Three concentric spherical shells are arranged as shown in the figure. The innermost and outermost spheres are connected to earth. If the middle sphere is given a charge $q_{0}$ . the charges induced in the innermost and outermost spheres respectively are

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MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Conductors in Electric Field

Consider an initially neutral hollow conducting spherical shell with inner radius $r$ and outer radius $2 r .$ A point charge $+ Q$ is now placed inside the shell at a distance $\frac{r}{2}$ from the center. The shell is then grounded by connecting the outer surface to the earth. P is an external point at a distance $2 r$ from the point charge $+ Q$ on the line passing through the center and the point charge $+ Q$ as shown in the figure.

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The magnitude of the force on a test charge $+ q$ placed at P will be

Important Questions on Electrostatics

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