Electric Potential Due to Shell

Q. Inside a hollow charged spherical conductor, the potential

1. Is constant
2. Varies directly as the distance from the centre
3. Varies inversely as the distance from the centre
4. Varies inversely as the square of the distance from the centre

Q.

A charged spherical conductor has potential of 6V and its radius is 2m. The electric intensity at its centre is :

1. zero

2. 3 N/C

3. 12 N/C

4. none of the above

Q. Three concentric spheres are shown in figure. Find the potential on surface of shell $B$. Charge on $A$, $B$ and $C$ are $3Q,-2Q$ and $Q$ respectively.

1. $\frac{3kQ}{5R}$
2. $\frac{4kQ}{3R}$
3. $\frac{3kQ}{4R}$
4. $\frac{3kQ}{2R}$

Q. A hollow conducting sphere of radius R has a charge (+Q) on its surface. What is the electric potential within the sphere at a distance $r=\frac{R}{3}$ from its centre

1. Zero
2. $\frac{1}{4\pi {ϵ}_0}\frac{Q}{r}$
3. $\frac{1}{4\pi {ϵ}_0}\frac{Q}{R}$
4. $\frac{1}{4\pi {ϵ}_0}\frac{Q}{r^2}$

Q.

Two concentric shells A and B of radii a and b are given charged $q_A$ and $A_B$.
(a) Find the potential difference between the shells.
(b) What happens when they are connected by means of a conducting wire.

1. $k{q}_A(\frac{1}{a}-\frac{1}{b})$
2. $k{q}_A(\frac{1}{b}-\frac{1}{a})$
3. $2k{q}_A(\frac{1}{a}-\frac{1}{b})$
4. $k{q}_A\left(\frac{1}{a}\right)$

Q. An annular disc of inner radius $a$ and outer radius $2a$ is uniformly charged with uniform surface charge density $\sigma$. Find the potential at a distance $a$ from the centre at a point $P$ lying on the axis which is perpendicular to the plane containing the disc.

1. $\frac{\sigma }{{ϵ}_0}a(\sqrt{5}-\sqrt{2})$
   
2. $\frac{\sigma }{2{ϵ}_0}a(\sqrt{5}-\sqrt{2})$
3. $\frac{\sigma }{2{ϵ}_0}(\sqrt{3}-\sqrt{2})$
   
4. $$\frac{\sigma }{2{ϵ}_0}a$$
   

Q. Potential difference between centre and surface of the non conducting sphere of radius $R$ and uniform volume charge density $\rho$ within it will be

1. $\frac{\rho R^2}{2{ϵ}_0}$
2. $\frac{\rho R^2}{3{ϵ}_0}$
3. $\frac{\rho R^2}{6{ϵ}_0}$
4. $\frac{\rho R^2}{4{ϵ}_0}$

Q. A point charge q is placed inside a conducting spherical shell of inner radius 2R and outer radius 3R at a distance of R from the centre of the shell. The electric potential at the centre of shell will be $\frac{1}{4\pi {ϵ}_0}$ times:

1. $\frac{q}{2R}$
2. $\frac{4q}{3R}$
3. $\frac{5q}{6R}$
4. $\frac{2q}{3R}$

Q. Three concentric shells A, B and C have radii R, 2R and 3R. A is given a charge q, C a charge 2q and B is grounded. Find the charge distributions on all the surfaces. Try the question yourself and see video for answer.

1. See Video
2. Watch the video
3. Play video
4. Refer video

Q. A solid sphere of radius $R$ has total charge $Q$, uniformly distributed. Find the minimum work done to decrease the radius of the sphere to $\frac{R}{2}$.

1. $\frac{2}{5}\frac{K{Q}^2}{R}$
2. $\frac{1}{5}\frac{K{Q}^2}{R}$
3. $\frac{3}{5}\frac{K{Q}^2}{R}$
4. $\frac{6}{5}\frac{K{Q}^2}{R}$

Q. Two insulated charged conducting spheres of radii 20 cm and 15 cm respectively and having an equal charge of 10 C are connected by a copper wire and then they are separated. Then

1. Both the spheres will have the same charge of 10 C
2. Surface charge density on the 20 cm sphere will be greater than that on the 15 cm sphere
3. Surface charge density on the 15 cm sphere will be greater than that on the 20 cm sphere
4. Surface charge density on the two spheres will be equal

Q. There is a hollow sphere of charge Q and radius R. The self-potential energy of the sphere is proportional to (charge)and (radius).

1. $Q$
2. $Q^2$
3. $\frac{1}{R}$
4. $\frac{1}{R^2}$

Q. A hollow metallic sphere of radius R is given a charge Q. The potential at its centre is

1. $Zero$
2. $\frac{1}{4\pi {ϵ}_0}.\frac{Q}{R}$
3. $\frac{1}{4\pi {ϵ}_0}.\frac{2Q}{R}$
4. $\frac{1}{4\pi {ϵ}_0}.\frac{Q}{2R}$

Q. A conducting sphere $\text{A}$ of radius $a$, with charge $Q$, is placed concentrically inside a conducting shell $\text{B}$ of radius $b$. $\text{B}$ is earthed and $\text{C}$ is the common center of $\text{A}$ and $\text{B}$. Study the following statements.

$\text{I.}$ The potential at a distance $r$ from $\text{C}$, where $a\le r\le b$, is $\frac{1}{4\pi {ϵ}_0}\left(\frac{Q}{r}\right)$
$\text{II.}$ The potential difference between $\text{A}$ and $\text{B}$ is $\frac{Q}{4\pi {ϵ}_0}(\frac{1}{a}-\frac{1}{b})$
$\text{III.}$The potential at a distance $r$ from $\text{C}$, where $a\le r\le b$, is $\frac{Q}{4\pi {ϵ}_0}(\frac{1}{r}-\frac{1}{b})$


Which of the following statements are correct?

1. Only $\text{(I)}$ and $\text{(II)}$
2. Only $\text{(II)}$ and $\text{(III)}$
3. Only $\text{(I)}$ and $\text{(III)}$
4. All

Q. Inside a hollow charged spherical conductor, the potential

1. Is constant
2. Varies directly as the distance from the centre
3. Varies inversely as the distance from the centre
4. Varies inversely as the square of the distance from the centre

Q. A hollow conducting sphere of radius R has a charge (+Q) on its surface. What is the electric potential within the sphere at a distance $r=\frac{R}{3}$ from its centre

1. Zero
2. $\frac{1}{4\pi {ϵ}_0}\frac{Q}{r}$
3. $\frac{1}{4\pi {ϵ}_0}\frac{Q}{R}$
4. $\frac{1}{4\pi {ϵ}_0}\frac{Q}{r^2}$

Q. The amount of work done in moving a point charge of 10C from the point A to B, inside a spherical shell as shown is .

1. 10 J
2. 20 J
3. 15 J
4. 0 J

Q. A concentric spherical cavity is cut out from a solid conducting sphere and a charge $+Q$ is placed at the centre of the cavity. The magnitude of net electric field $E$ and net potential $V$ at point $A$ is
[$k=\frac{1}{4\pi {ϵ}_0}$]

1. $E=\frac{4kQ}{R^2},V=\frac{kQ}{R}$
2. $E=\frac{4kQ}{R^2},V=\frac{3kQ}{2R}$
3. $E=\frac{kQ}{4R^2},V=\frac{kQ}{2R}$
4. $E=\frac{kQ}{R^2},V=0$

Q. If a charge Q is distributed on the concentric hollow spheres of radii r and R(> r) such that their surface densities are equal then the potential at their common centre is

1. $\frac{Q(R^2+r^2)}{4\pi {ϵ}_0(R+r)}$
2. $\frac{QR}{R+r}$
3. Zero
4. $\frac{Q(R+r)}{4\pi {ϵ}_0(R^2+r^2)}$

Q. A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 volt. The potential at the centre of the sphere is
(IIT-JEE 1983)

1. zero
2. 10 volt
3. same as at a point 5 cm away from the surface
4. same as at a point 25 cm away from the surface

Q. Three concentric spherical metallic shells A, B and C of radii $a,b$ and $c(a<b<c)$ have surface charge densities $\sigma ,-\sigma$ and $\sigma ,$ respectively.
If shells A and C are at the same potential, the relation between the radii $a,b$ and $c$ is

1. $a=b+c$
2. $c=a+b$
3. $b=a+c$
4. $2a=b-c$

Q. Three concentric shells A, B and C have radii R, 2R and 3R. A is given a charge q, C a charge 2q and B is grounded. Find the charge distributions on all the surfaces. Try the question yourself and see video for answer.

1. See Video
2. Watch the video
3. Play video
4. Refer video

Q. Two metal spheres of radii in the ratio 3:4 are connected and a charge of 14$\mu$ C is given to the system and then they are separated so that there is no mutual force between them. The potential due to the larger sphere at a distance of 3m from the centre of the sphere is

1. 72KV
2. 36KV
3. 24KV
4. 12KV

Q. Two concentric spherical conducting shells of radii $R$ and $2R$ carry charges $Q$ and $2Q$ respectively. Change in electric potential on the outer shell when both are connected by a conducting wire is:
(Where $K=\frac{1}{4\pi {ϵ}_0}$)

1. Zero
2. $\frac{KQ}{R}$
3. $\frac{3KQ}{2R}$
4. $\frac{2KQ}{R}$

Q. There are four concentric shells A, B, C and D of radii a, 2a, 3a and 4a respectively. Shells B and D are given charges +q and –q respectively. Shell C is now earthed. The potential difference $V_A-V_C$ is :

1. $\frac{kq}{2a}$
2. $\frac{kq}{3a}$
3. $\frac{kq}{4a}$
4. $\frac{kq}{6a}$

Q. Two thin conducting shells of radii $R$ and $3R$ are shown in the figure. The outer shell carries a charge $+Q$ and the inner shell is neutral. The inner shell is earthed with the help of a switch $S$.

1. With the switch $S$ open, the potential of the inner sphere is equal to that of the outer
2. With the switch $S$ closed, the charge attained by the inner sphere is $-1/3$ times that of charge present on the outer sphere.
3. When the switch $S$ is closed, the potential of the inner sphere becomes zero
4. By closing the switch the capacitance of the system increases

Q. Figure shows two conducting thin concentric shells of radii $r$ and $3r$. The outer shell carries $q$ while inner shell is neutral and is connected to earth by a switch $S$. Find the charge that will flow from earth to inner shell after the switch $S$ is closed.

1. $-\frac{q}{3}$
2. $-\frac{q}{2}$
3. $\frac{2q}{3}$
4. $\frac{q}{3}$

Q.

Three concentric metallic spherical shell A, B and C or radii a, b and c (a < b < c) have surface charge densities $-\sigma$, $+\sigma$ and $-\sigma$ respectively. The potential of shell A is :

1. $\frac{\sigma }{{\epsilon }_0}$[a+b-c]
2. $\frac{\sigma }{{\epsilon }_0}$[a-b+c]
3. $\frac{\sigma }{{\epsilon }_0}$[b-a-c]
4. none

Q. Three concentric spheres are shown in figure. Find the potential on surface of shell $B$. Charge on $A$, $B$ and $C$ are $3Q,-2Q$ and $Q$ respectively.

1. $\frac{3kQ}{5R}$
2. $\frac{4kQ}{3R}$
3. $\frac{3kQ}{4R}$
4. $\frac{3kQ}{2R}$

Q. A spherical conductor of radius $R$ is charged with $Q$ units of negative charge. The escape velocity of a particle of mass $m$ and charge $q$ from the surface of this conductor is

1. $\sqrt{\frac{Qq}{2\pi {ϵ}_{0}mR}}$
2. $\sqrt{\frac{Qq}{4\pi {ϵ}_{0}R}}$
3. $\sqrt{\frac{Qq}{4\pi {ϵ}_{0}m{R}^2}}$
4. Escape is not possible.