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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359426 A solid spherical conductor of radius $R$ has a spherical cavity of radius $a (a < R)$ at its centre.
A charge $+ Q$ is kept at the centre. The charge at the inner surface, outer and at a position $r (a < r < R)$ are respectively

1

+ Q, - Q, 0

2

- Q, + Q, 0

3

0, - Q, 0

4

+ Q, 0, 0

Explanation:

The charge at the inner surface, outer surface and inside the conductor at $P = (- Q, + Q, 0)$ as shown in the figure
supporting img

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359427 Consider two concentric spherical shells of radii $R$ and 2 $R$ . The shell $A$ is given charge $q$ and shell $B$ charge $- q$ . Then find the charge on the outer surface of $B$ .
supporting img

1

0

2

q

3

- q

4

2 q

Explanation:

The charge distribution on the surfaces are shown in the figure. The charge on the outer surface of the inner shell is $q$ and charge on the inner surface of the outer shell is $- q$ (from Gauss law)
supporting img
The charge on outer surface of shell $B$ is zero.

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359428 A metallic spherical shell has an inner radius $R_{1}$ and outer radius $R_{2}$ . A charge is placed at the centre of the spherical cavity. The surface charge density on the inner surface is
supporting img

1

\frac{q}{4 π R_{1}^{2}}

2

\frac{- q}{4 π R_{1}^{2}}

3

\frac{q^{2}}{4 π R_{2}^{2}}

4

\frac{q}{4 π R_{2}^{2}}

Explanation:

When a charge $+ q$ is placed at the centre of spherical cavity as shown in figure.
supporting img
Charge induced on the inner surface of shell
$\begin{matrix} (1) & = - q \end{matrix}$
Charge induced on the outer surface of shell
$\begin{matrix} (2) & = + q \end{matrix}$
$∴$ Surface charge density on the inner surface
$= \frac{- q}{4 π R_{1}^{2}}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359429 A metal sphere $A$ of radius $a$ is charged to potential $V$ . What will be its potential if it is enclosed by a spherical conducting shell $B$ of radius $b$ and the two are connected by a wire?
supporting img

1

\frac{a}{b} V

2

V

3

\frac{b}{a} V

4

0

Explanation:

If the charge on sphere of radius $a$ is $q$ ,
$V = \frac{1}{4 π ε_{0}} \frac{q}{a}$
i.e., $q = (4 π ε_{0} a) V$ (1)
Now, when sphere $A$ is enclosed by spherical conductor $B$ and the two are connected by a wire, charge flows to the outer surface of $B$ because electrostatics repulsion and so that potential of $B$ will be $V_{B} = \frac{1}{4 π ε_{0}} \frac{q}{b}$
$V_{B} = \frac{1}{4 π ε_{0}} \frac{4 π ε_{0} a}{b} V = \frac{a}{b} V$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359430 A spherical conducting shell with an inner radius 2 $R$ and outer radius 3 $R$ surrounds a spherical shell of radius $R$ . If $q$ and 2 $q$ are the charges given to the two shells then find the charge present on the outer surface of the outer shell.
supporting img

1

3 q

2

q

3

0

4

2 q

Explanation:

The charge distribution is shown for all the surfaces. The charge on the inner shell must be equal to $q$ . From Gauss law charge on the inner surface of the outer shell is $- q$ . From conservation of charge the charge on the outer surface is $3 q$ .
supporting img

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359426 A solid spherical conductor of radius $R$ has a spherical cavity of radius $a (a < R)$ at its centre.
A charge $+ Q$ is kept at the centre. The charge at the inner surface, outer and at a position $r (a < r < R)$ are respectively

1

+ Q, - Q, 0

2

- Q, + Q, 0

3

0, - Q, 0

4

+ Q, 0, 0

Explanation:

The charge at the inner surface, outer surface and inside the conductor at $P = (- Q, + Q, 0)$ as shown in the figure
supporting img

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359427 Consider two concentric spherical shells of radii $R$ and 2 $R$ . The shell $A$ is given charge $q$ and shell $B$ charge $- q$ . Then find the charge on the outer surface of $B$ .
supporting img

1

0

2

q

3

- q

4

2 q

Explanation:

The charge distribution on the surfaces are shown in the figure. The charge on the outer surface of the inner shell is $q$ and charge on the inner surface of the outer shell is $- q$ (from Gauss law)
supporting img
The charge on outer surface of shell $B$ is zero.

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359428 A metallic spherical shell has an inner radius $R_{1}$ and outer radius $R_{2}$ . A charge is placed at the centre of the spherical cavity. The surface charge density on the inner surface is
supporting img

1

\frac{q}{4 π R_{1}^{2}}

2

\frac{- q}{4 π R_{1}^{2}}

3

\frac{q^{2}}{4 π R_{2}^{2}}

4

\frac{q}{4 π R_{2}^{2}}

Explanation:

When a charge $+ q$ is placed at the centre of spherical cavity as shown in figure.
supporting img
Charge induced on the inner surface of shell
$\begin{matrix} (1) & = - q \end{matrix}$
Charge induced on the outer surface of shell
$\begin{matrix} (2) & = + q \end{matrix}$
$∴$ Surface charge density on the inner surface
$= \frac{- q}{4 π R_{1}^{2}}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359429 A metal sphere $A$ of radius $a$ is charged to potential $V$ . What will be its potential if it is enclosed by a spherical conducting shell $B$ of radius $b$ and the two are connected by a wire?
supporting img

1

\frac{a}{b} V

2

V

3

\frac{b}{a} V

4

0

Explanation:

If the charge on sphere of radius $a$ is $q$ ,
$V = \frac{1}{4 π ε_{0}} \frac{q}{a}$
i.e., $q = (4 π ε_{0} a) V$ (1)
Now, when sphere $A$ is enclosed by spherical conductor $B$ and the two are connected by a wire, charge flows to the outer surface of $B$ because electrostatics repulsion and so that potential of $B$ will be $V_{B} = \frac{1}{4 π ε_{0}} \frac{q}{b}$
$V_{B} = \frac{1}{4 π ε_{0}} \frac{4 π ε_{0} a}{b} V = \frac{a}{b} V$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359430 A spherical conducting shell with an inner radius 2 $R$ and outer radius 3 $R$ surrounds a spherical shell of radius $R$ . If $q$ and 2 $q$ are the charges given to the two shells then find the charge present on the outer surface of the outer shell.
supporting img

1

3 q

2

q

3

0

4

2 q

Explanation:

The charge distribution is shown for all the surfaces. The charge on the inner shell must be equal to $q$ . From Gauss law charge on the inner surface of the outer shell is $- q$ . From conservation of charge the charge on the outer surface is $3 q$ .
supporting img

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359426 A solid spherical conductor of radius $R$ has a spherical cavity of radius $a (a < R)$ at its centre.
A charge $+ Q$ is kept at the centre. The charge at the inner surface, outer and at a position $r (a < r < R)$ are respectively

1

+ Q, - Q, 0

2

- Q, + Q, 0

3

0, - Q, 0

4

+ Q, 0, 0

Explanation:

The charge at the inner surface, outer surface and inside the conductor at $P = (- Q, + Q, 0)$ as shown in the figure
supporting img

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359427 Consider two concentric spherical shells of radii $R$ and 2 $R$ . The shell $A$ is given charge $q$ and shell $B$ charge $- q$ . Then find the charge on the outer surface of $B$ .
supporting img

1

0

2

q

3

- q

4

2 q

Explanation:

The charge distribution on the surfaces are shown in the figure. The charge on the outer surface of the inner shell is $q$ and charge on the inner surface of the outer shell is $- q$ (from Gauss law)
supporting img
The charge on outer surface of shell $B$ is zero.

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359428 A metallic spherical shell has an inner radius $R_{1}$ and outer radius $R_{2}$ . A charge is placed at the centre of the spherical cavity. The surface charge density on the inner surface is
supporting img

1

\frac{q}{4 π R_{1}^{2}}

2

\frac{- q}{4 π R_{1}^{2}}

3

\frac{q^{2}}{4 π R_{2}^{2}}

4

\frac{q}{4 π R_{2}^{2}}

Explanation:

When a charge $+ q$ is placed at the centre of spherical cavity as shown in figure.
supporting img
Charge induced on the inner surface of shell
$\begin{matrix} (1) & = - q \end{matrix}$
Charge induced on the outer surface of shell
$\begin{matrix} (2) & = + q \end{matrix}$
$∴$ Surface charge density on the inner surface
$= \frac{- q}{4 π R_{1}^{2}}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359429 A metal sphere $A$ of radius $a$ is charged to potential $V$ . What will be its potential if it is enclosed by a spherical conducting shell $B$ of radius $b$ and the two are connected by a wire?
supporting img

1

\frac{a}{b} V

2

V

3

\frac{b}{a} V

4

0

Explanation:

If the charge on sphere of radius $a$ is $q$ ,
$V = \frac{1}{4 π ε_{0}} \frac{q}{a}$
i.e., $q = (4 π ε_{0} a) V$ (1)
Now, when sphere $A$ is enclosed by spherical conductor $B$ and the two are connected by a wire, charge flows to the outer surface of $B$ because electrostatics repulsion and so that potential of $B$ will be $V_{B} = \frac{1}{4 π ε_{0}} \frac{q}{b}$
$V_{B} = \frac{1}{4 π ε_{0}} \frac{4 π ε_{0} a}{b} V = \frac{a}{b} V$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359430 A spherical conducting shell with an inner radius 2 $R$ and outer radius 3 $R$ surrounds a spherical shell of radius $R$ . If $q$ and 2 $q$ are the charges given to the two shells then find the charge present on the outer surface of the outer shell.
supporting img

1

3 q

2

q

3

0

4

2 q

Explanation:

The charge distribution is shown for all the surfaces. The charge on the inner shell must be equal to $q$ . From Gauss law charge on the inner surface of the outer shell is $- q$ . From conservation of charge the charge on the outer surface is $3 q$ .
supporting img

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359426 A solid spherical conductor of radius $R$ has a spherical cavity of radius $a (a < R)$ at its centre.
A charge $+ Q$ is kept at the centre. The charge at the inner surface, outer and at a position $r (a < r < R)$ are respectively

1

+ Q, - Q, 0

2

- Q, + Q, 0

3

0, - Q, 0

4

+ Q, 0, 0

Explanation:

The charge at the inner surface, outer surface and inside the conductor at $P = (- Q, + Q, 0)$ as shown in the figure
supporting img

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359427 Consider two concentric spherical shells of radii $R$ and 2 $R$ . The shell $A$ is given charge $q$ and shell $B$ charge $- q$ . Then find the charge on the outer surface of $B$ .
supporting img

1

0

2

q

3

- q

4

2 q

Explanation:

The charge distribution on the surfaces are shown in the figure. The charge on the outer surface of the inner shell is $q$ and charge on the inner surface of the outer shell is $- q$ (from Gauss law)
supporting img
The charge on outer surface of shell $B$ is zero.

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359428 A metallic spherical shell has an inner radius $R_{1}$ and outer radius $R_{2}$ . A charge is placed at the centre of the spherical cavity. The surface charge density on the inner surface is
supporting img

1

\frac{q}{4 π R_{1}^{2}}

2

\frac{- q}{4 π R_{1}^{2}}

3

\frac{q^{2}}{4 π R_{2}^{2}}

4

\frac{q}{4 π R_{2}^{2}}

Explanation:

When a charge $+ q$ is placed at the centre of spherical cavity as shown in figure.
supporting img
Charge induced on the inner surface of shell
$\begin{matrix} (1) & = - q \end{matrix}$
Charge induced on the outer surface of shell
$\begin{matrix} (2) & = + q \end{matrix}$
$∴$ Surface charge density on the inner surface
$= \frac{- q}{4 π R_{1}^{2}}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359429 A metal sphere $A$ of radius $a$ is charged to potential $V$ . What will be its potential if it is enclosed by a spherical conducting shell $B$ of radius $b$ and the two are connected by a wire?
supporting img

1

\frac{a}{b} V

2

V

3

\frac{b}{a} V

4

0

Explanation:

If the charge on sphere of radius $a$ is $q$ ,
$V = \frac{1}{4 π ε_{0}} \frac{q}{a}$
i.e., $q = (4 π ε_{0} a) V$ (1)
Now, when sphere $A$ is enclosed by spherical conductor $B$ and the two are connected by a wire, charge flows to the outer surface of $B$ because electrostatics repulsion and so that potential of $B$ will be $V_{B} = \frac{1}{4 π ε_{0}} \frac{q}{b}$
$V_{B} = \frac{1}{4 π ε_{0}} \frac{4 π ε_{0} a}{b} V = \frac{a}{b} V$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359430 A spherical conducting shell with an inner radius 2 $R$ and outer radius 3 $R$ surrounds a spherical shell of radius $R$ . If $q$ and 2 $q$ are the charges given to the two shells then find the charge present on the outer surface of the outer shell.
supporting img

1

3 q

2

q

3

0

4

2 q

Explanation:

The charge distribution is shown for all the surfaces. The charge on the inner shell must be equal to $q$ . From Gauss law charge on the inner surface of the outer shell is $- q$ . From conservation of charge the charge on the outer surface is $3 q$ .
supporting img

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359426 A solid spherical conductor of radius $R$ has a spherical cavity of radius $a (a < R)$ at its centre.
A charge $+ Q$ is kept at the centre. The charge at the inner surface, outer and at a position $r (a < r < R)$ are respectively

1

+ Q, - Q, 0

2

- Q, + Q, 0

3

0, - Q, 0

4

+ Q, 0, 0

Explanation:

The charge at the inner surface, outer surface and inside the conductor at $P = (- Q, + Q, 0)$ as shown in the figure
supporting img

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359427 Consider two concentric spherical shells of radii $R$ and 2 $R$ . The shell $A$ is given charge $q$ and shell $B$ charge $- q$ . Then find the charge on the outer surface of $B$ .
supporting img

1

0

2

q

3

- q

4

2 q

Explanation:

The charge distribution on the surfaces are shown in the figure. The charge on the outer surface of the inner shell is $q$ and charge on the inner surface of the outer shell is $- q$ (from Gauss law)
supporting img
The charge on outer surface of shell $B$ is zero.

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359428 A metallic spherical shell has an inner radius $R_{1}$ and outer radius $R_{2}$ . A charge is placed at the centre of the spherical cavity. The surface charge density on the inner surface is
supporting img

1

\frac{q}{4 π R_{1}^{2}}

2

\frac{- q}{4 π R_{1}^{2}}

3

\frac{q^{2}}{4 π R_{2}^{2}}

4

\frac{q}{4 π R_{2}^{2}}

Explanation:

When a charge $+ q$ is placed at the centre of spherical cavity as shown in figure.
supporting img
Charge induced on the inner surface of shell
$\begin{matrix} (1) & = - q \end{matrix}$
Charge induced on the outer surface of shell
$\begin{matrix} (2) & = + q \end{matrix}$
$∴$ Surface charge density on the inner surface
$= \frac{- q}{4 π R_{1}^{2}}$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359429 A metal sphere $A$ of radius $a$ is charged to potential $V$ . What will be its potential if it is enclosed by a spherical conducting shell $B$ of radius $b$ and the two are connected by a wire?
supporting img

1

\frac{a}{b} V

2

V

3

\frac{b}{a} V

4

0

Explanation:

If the charge on sphere of radius $a$ is $q$ ,
$V = \frac{1}{4 π ε_{0}} \frac{q}{a}$
i.e., $q = (4 π ε_{0} a) V$ (1)
Now, when sphere $A$ is enclosed by spherical conductor $B$ and the two are connected by a wire, charge flows to the outer surface of $B$ because electrostatics repulsion and so that potential of $B$ will be $V_{B} = \frac{1}{4 π ε_{0}} \frac{q}{b}$
$V_{B} = \frac{1}{4 π ε_{0}} \frac{4 π ε_{0} a}{b} V = \frac{a}{b} V$

PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359430 A spherical conducting shell with an inner radius 2 $R$ and outer radius 3 $R$ surrounds a spherical shell of radius $R$ . If $q$ and 2 $q$ are the charges given to the two shells then find the charge present on the outer surface of the outer shell.
supporting img

1

3 q

2

q

3

0

4

2 q

Explanation:

The charge distribution is shown for all the surfaces. The charge on the inner shell must be equal to $q$ . From Gauss law charge on the inner surface of the outer shell is $- q$ . From conservation of charge the charge on the outer surface is $3 q$ .
supporting img