Conductors

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JEE Main 2019

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 is a dipole $p$ as shown. In this case,

surface charge density on the inner surface is uniform and equal to

\frac{Q /2}{4 π a ^{2}}

(B)

electric field outside the shell is the same as that of a point charge at the centre of the shell

(C)

surface charge density on the outer surface depends on

∣ p ∣

(D)

surface charge density on the inner surface of the shell is zero everywhere

LEVELJEE Advanced

Three concentric metallic spherical shells of radii $R, 2 R$ and $3 R$ are given charges $Q_{1}, Q_{2}$ and $Q_{3}$ , respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, $Q_{1} : Q_{2} : Q_{3}$ , is

(A)

1 : 2 : 3

(B)

1 : 3 : 5

(C)

1 : 4 : 9

(D)

1 : 8 : 18

JEE Advanced 1998

LEVELJEE Advanced

A conducting sphere $S_{1}$ of radius $r$ is attached to an insulating handle. Another conducting sphere $S_{2}$ of radius $R$ is mounted on an insulating stand. $S_{2}$ is initially uncharged. $S_{1}$ is given a charge $Q$ , brought into contact with $S_{2}$ and removed. $S_{1}$ is recharged such that the charge on it is again $Q$ and it is again brought into contact with $S_{2}$ and removed. This procedure is repeated $n$ times. (a) Find the electrostatic energy of $S_{2}$ after $n$ such contacts with $S_{1}$ . (b) What is the limiting value of this energy as $n \to \infty$ ?

JEE Advanced 2007

LEVELBoard

Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then

(A)

negative and distributed uniformly over the surface of the sphere

(B)

negative and appears only at the point on the sphere closest to the point charge

(C)

negative and distributed non-uniformly over the entire surface of the sphere

(D)

zero

LEVELBoard

Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then

(A)

negative and distributed uniformly over the surface of the sphere

(B)

negative and appears only at the point on the sphere closest to the point charge

(C)

negative and distributed non-uniformly over the entire surface of the sphere

A metallic shell has a point charge $q$ kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces ?

A spherical metal shell $A$ of radius $R_{A}$ and a solid metal sphere $B$ of radius $R_{B} (< R_{A})$ are kept far apart and each is given charge $+ Q$ . Now they are connected by a thin metal wire. Then

* Multiple Correct Options

(A)

E_{A}^{inside} = 0

(B)

Q_{A} > Q_{B}

(C)

\frac{σ _{A}}{σ _{B}} = \frac{R _{B}}{R _{A}}

(D)

E_{A}^{on surface} < E_{B}^{on surface}

LEVELJEE Main

An elliptical cavity is carved within a perfect conductor. A positive charge $q$ is placed at the centre of the cavity. The points $A$ and $B$ are on the cavity surface as shown in the figure. Then

* Multiple Correct Options

(A)

electric field near

A

in the cavity = electric field near

B

in the cavity.

(B)

charge density at

A

= charge density at

B

(C)

potential at

A

= potential at

B

(D)

total electric field flux through the surface of the cavity is

q / ε_{0}

JEE Advanced 1996

LEVELJEE Main

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

A positive point charge of $1 0^{- 8} C$ is kept at a distance of $20 cm$ from the center of a neutral conducting sphere of radius $10 cm$ . The sphere is then grounded and the charge on the sphere is measured. The grounding is then removed and subsequently the point charge is moved by a distance of $10 cm$ further away from the center of the sphere along the radial direction. Taking $\frac{1}{4 π ϵ _{0}} = 9 \times 1 0^{9} Nm^{2} / C^{2}$ (where $ϵ_{0}$ is the permittivity of free space), which of the following statements is/are correct:

* Multiple Correct Options

(A)

Before the grounding, the electrostatic potential of the sphere is

450 V

(B)

Charge flowing from the sphere to the ground because of grounding is

5 \times 1 0^{- 9} C

(C)

After the grounding is removed, the charge on the sphere is

- 5 \times 1 0^{- 9} C

(D)

The final electrostatic potential of the sphere is

300 V

LEVELJEE Main

Two spherical conductors $A$ and $B$ of radii $1 mm$ and $2 mm$ are separated by a distance of $5 cm$ and are uniformly charged. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres $A$ and $B$ is

(A)

4 : 1

(B)

1 : 2

(C)

2 : 1

(D)

1 : 4

JEE Main 2020

LEVELJEE Main

Two isolated conducting spheres $S_{1}$ and $S_{2}$ of radii $\frac{2}{3} R$ and $\frac{1}{3} R$ , have charges $12 μ C$ and $- 3 μ C$ respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done, the charges on $S_{1}$ and $S_{2}$ respectively, are

(A)

4.5 μ C

on both

(B)

+ 4.5 μ C

and

- 4.5 μ C

(C)

3 μ C

and

6 μ C

(D)

6 μ C

and

3 μ C

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } 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 is a dipole p as shown. In this case,

Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then

Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A metallic shell has a point charge q kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces ?

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

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 is a dipole $p$ as shown. In this case,

A metallic shell has a point charge $q$ kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces ?