In the figure, two conducting concentric spherical shells are shown.

                           

If the electric potential at the centre is 20V and the electric potential at the surface of outer shell is 5V, then the potential at the surface of inner shell is –

1.  5V                   

2.  15V 

3.  20V                 

3.  cannot be determined as radii are not given

At the mid point of a line joining an electron and a proton, the values of E and V will be.

1. $\mathrm{E}=0, \mathrm{V}\ne 0$                   

2. $\mathrm{E}\ne 0, \mathrm{V}=0$

3. $\mathrm{E}\ne 0, \mathrm{V}\ne 0$                   

4. $\mathrm{E}=0, \mathrm{V}=0$

Two point charge of $8 \mathrm{\mu C}$ and $12 \mathrm{\mu C}$ are kept in air at a distance of 10 cm from each other. The work required to change the distance between them to 6 cm will be.

1.  $5.8 \mathrm{J}$                       

2.  $4.8 \mathrm{J}$

3.  $3.8 \mathrm{J}$                       

4.  $2.8 \mathrm{J}$

Maximum charge stored on a metal sphere of radius $15$ cm may be $7.5 \mu \mathrm{C}$. The potential energy of the sphere in this case is :

1.  $9.67 \mathrm{J}$                   

2.  $0.25 \mathrm{J}$ 

3.  $3.25 \mathrm{J}$                    

4.  $1.69 \mathrm{J}$

Four identical particles each of mass m and charge q are kept at the four corners of a square of length L. The final velocity of these particles after setting them free will be.

1. ${\left[\frac{{\mathrm{Kq}}^2}{\mathrm{mL}}\left(5.4\right)\right]}^{1/2}$                           

2. ${\left[\frac{{\mathrm{Kq}}^2}{\mathrm{mL}}\left(1.35\right)\right]}^{1/2}$

3. ${\left[\frac{{\mathrm{Kq}}^2}{\mathrm{mL}}\left(2.7\right)\right]}^{1/2}$                           

4. Zero

A charge $+\mathrm{Q}$ is uniformly distributed over a thin ring of radius $\mathrm{R}$, velocity of an electron at the moment it passes through the centre $\mathrm{O}$ of the ring, if the electron was initially at rest at a point $\mathrm{A}$ which is very far away from the centre and on the axis of the ring is

1. $\sqrt{\frac{2\mathrm{kQe}}{\mathrm{mR}}}$                     

2. $\sqrt{\frac{\mathrm{kQe}}{\mathrm{m}}}$

3. $\sqrt{\frac{\mathrm{kme}}{\mathrm{QR}}}$                       

4. $\sqrt{\frac{\mathrm{kQe}}{\mathrm{mR}}}$

${10}^3$ small water drops, each of radius r and each carrying charge q, combine to form one bigger drop. The potential of a bigger drop as compared to that of a smaller drop will be.

1.  ${10}^5 \mathrm{V}$                     

2.  ${10}^3 \mathrm{V}$

3.  $10 \mathrm{V}$                       

4.  ${10}^2 \mathrm{V}$

Infinite charges, each of q coulomb are lying on the x-axis at x = 1m, 2m, 4m, 8m, --------.The electric potential due to these charges at x = 0 will be – 

1. $\mathrm{Kq}$                   

2. $\frac{\mathrm{Kq}}{2}$ 

3. $2 \mathrm{Kq}$                 

4. $\frac{\mathrm{Kq}}{3}$

The plates of a parallel plate capacitor have an area of $90 {\mathrm{cm}}^2$ each and are separated by $2.5 \mathrm{mm}$. The capacitor is charged by a 400 volt supply. How much electrostatic energy is stored by the capacitor?

1.  $2.55\times {10}^{-6} \mathrm{J}$                         

2.  $1.55\times {10}^{-6} \mathrm{J}$

3.  $8.15\times {10}^{-6} \mathrm{J}$                         

4.  $5.5\times {10}^{-6} \mathrm{J}$

An alpha particle with kinetic energy $10 \mathrm{MeV}$ is heading towards a stationary nucleus of atomic number $50$. Calculate the distance of closest approach.

1.  $1.4\times {10}^{-15} \mathrm{m}$                         

2.  $4\times {10}^{-15} \mathrm{m}$

3.  $14.4\times {10}^{-15} \mathrm{m}$                       

4.  $8\times {10}^{-15} \mathrm{m}$