Electric Potential Due to Shell

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. 40 V
4. 80 V

Q. If the electric potential of the inner shell is $20\text{V}$ and that of the outer shell is $10\text{V}$, then the potential at the centre will be (in $\text{V}$):
[Assume both thin shells to be conducting]

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

1. $Zero$
2. $\frac{Q(R^2+r^2)}{4\pi {ϵ}_0(R+r)}$
   
3. $\frac{QR}{R+r}$
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. same as at a point 5 cm away from the surface
3. 10 volt
4. same as at a point 25 cm away from the surface

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


Spherical shell

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

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

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

Q. Two conducting spheres of radii a and b respectively are charged and joined by a wire. The ratio of electric field due the spheres at their surfaces when isolated is

1. $\frac{b}{a}$
2. $\frac{a^2}{b^2}$
3. $\frac{a}{b}$
4. $\frac{b^2}{a^2}$

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