Electric Potential Due to Shell

Q. The potential at a distance $R/2$ from the centre of a conducting sphere of radius $R$ containing charge $Q$ will be

1. $\frac{Q}{2\pi {ϵ}_{0}R}$
2. $\frac{Q}{8\pi {ϵ}_{0}R}$
3. $0$
4. $\frac{Q}{4\pi {ϵ}_{0}R}$

Q. The electric field due to a uniformly charged non conducting solid sphere with charge 10 C at a point 2 cm from its centre is? Radius is 1cm.

Q. If we take potential at the solid surface = 0 then find potential at centre and infinity

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.

Q. if the potential at the surface of a uniform sphere of mass M and radius R is 0, then potential at its centre would be

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

Q. If the potential at the surface of uniformsphere of mass M and radius R is zero, then potentialat infinity would be 1.GM/R 2.-GM/2R 3.-GM/4R

Q.

If a unit charge is taken from one part to another part over an equipotential surface, then what is the change in electrostatic potential energy of the charge?

Q. A solid conducting sphere of radius $a$ is surrounded by a thin uncharged concentric conducting shell of radius $2a$. A point charge $q$ is placed at a distance $4a$ from common centre of conducting sphere and shell. The inner sphere is then grounded.


The potential of outer shell is:

1. $\frac{q}{8\pi {ϵ}_{0}a}$
2. $\frac{q}{16\pi {ϵ}_{0}a}$
3. $\frac{q}{32\pi {ϵ}_{0}a}$
4. $\frac{q}{4\pi {ϵ}_{0}a}$

Q. A spherical conductor of radius 2m is charged to a potential of 120 V. It is now placed inside another hollow spherical conductor of radius 6m. Calculate the potential to which the bigger sphere would be raised to?

1. 20 V
2. 60 V
3. 80 V
4. 40 V

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. Figure shows three circular arcs, each of radius $R$ and charges $+Q,-2Q$ and $3Q$ are present in respective arcs.


The net electric potential at the centre of curvature is

1. $\frac{2kQ}{R}$
2. $\frac{8kQ}{R}$
3. $\frac{kQ}{R}$
4. $\frac{kQ}{2R}$

Q. Equal charges are given to two conducting spheres of different radii. The potential will be

1. more on the smaller sphere
2. more on the bigger sphere
3. equal on both the spheres
4. Dependent on the nature of the materials of the spheres

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 $V_A,V_B$ and $V_C$ are potential of shells A, B and C, respectively, match the columns
$\begin{array}{cc}\text{Column A}& \text{Column B}\\ \text{a.}{V}_A& \text{i.}\frac{\sigma }{{\epsilon }_0}\left[\frac{a^2-b^2+c^2}{c}\right]\\ \text{b.}{V}_B& \text{ii.}\frac{\sigma }{{\epsilon }_0}[\frac{a^2}{b}-b+c]\\ \text{c.}{V}_C& \text{iii.}\frac{\sigma }{{\epsilon }_0}[a-b+c]\end{array}$

1. a − iii, b − ii, c − i
2. a − ii, b − iii, c − i
3. a − i, b − ii, c − iii
4. a − iii, b − i, c − ii

Q. Repeat the previous problem with all conditions remaining the same as before and A and C connected by means of a conducting wire.

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

Q.

Two concentric shells A and B have radii a and b. A is given a charge q and B is grounded. Find the potential difference between the shells.

1. $\frac{kq}{b}\left[\frac{b-a}{b}\right]$

2. $\frac{k}{b}\left[\frac{b-a}{b}\right]$

3. $\frac{kq}{b}\left[\frac{a-b}{b}\right]$

4. $\frac{k{q}^2}{b}\left[\frac{a-b}{b}\right]$

Q. A solid conducting sphere of 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

1. V
2. 2 V
3. 4 V
4. - 2 V

Q. Two concentric spheres of radius 20 cm & 40 cm are arranged as shown is figure. Potential difference between spheres is:

1. 20 volt
2. 30 volt
3. 10 volt
4. 0 volt

Q. A hollow metallic sphere of radius $10cm$ is given a charge of $3.2\times {10}^{-9}C$. The electric intensity at a point $4cm$ from the centre is

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. We have an isolated conducting spherical shell of radius $10cm$. Some positive charge is given to it so that resulting electric field has a maximum intensity of $1.8\times {10}^{6}N{C}^{-1}.$ The same amount of negative charge is given to another isolated conducting spherical shell of radius $20cm$. Now, first shell is placed inside the second so that both are concentric as shown in the figure.

The electric potential at any point inside the first shell is

1. $18\times {10}^{4}V$
2. $9\times {10}^{4}V$
3. $4.5\times {10}^{4}V$
4. $1.8\times {10}^{4}V$

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. Calculate the wavelength of an electron if it is travelling at a speed of $1.6\times {10}^8{\text{ms}}^{-1}$.

Mass of an electron $=9.1\times {10}^{-31}\text{kg}$

1. $4.5\times {10}^{-11}\text{m}$
2. $4.5\times {10}^{-12}\text{m}$
3. $4.5\times {10}^{-10}\text{m}$
4. $4.5\times {10}^{-13}\text{m}$

Q. The de-Broglie wavelength of proton travelling at velocity $v$ is same as the wavelength of an alpha particle. What is the velocity of the alpha particle ?

1. $\frac{v}{2}$
2. $\frac{v}{4}$
3. $4v$
4. $2v$

Q. A hollow metal sphere of radius 5 cm is charged so that the potential on its surface is 10 V. The potential at the centre of the sphere is

1. 0 V
2. 10 V
3. Same as at point 5 cm away from the surface
4. Same as at point 25 cm away from the surface

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. 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. An infinite conducting sheet has surface charge density $\sigma$. The distance between two equipotential surfaces is $r$. The potential difference between these two surfaces is

1. $\frac{\sigma r}{2{\epsilon }_0}$
2. $\frac{\sigma r}{{\epsilon }_0}$
3. $\frac{\sigma }{{\epsilon }_{0}r}$
4. $\frac{\sigma }{2{\epsilon }_{0}r}$

Q. Spherical cavity of spherical conductor has point $A$ inside conductor at distance $r$ from charge $Q$ & point $B$ is also inside conductor at distance $2r$ from charge $Q$, then

1. $V_A:V_B=1:2$
2. $V_A:V_B=2:1$
3. $V_A:V_B=4:1$
4. $V_A:V_B=1:1$

Q. Calculate the gravitational field intensity and potential at the centre of the base of a solid hemisphere of mass m radius r.