A proton and an $\mathrm{\alpha }$-particle are at a distance r from each other. After letting them free if they move to infinity, the kinetic energy of the proton will be -

1.  $8{\mathrm{Ke}}^2/5\mathrm{r}$                           

2.  $2{\mathrm{Ke}}^2/5\mathrm{r}$

3.  $8{\mathrm{Ke}}^2/\mathrm{r}$                             

4.  ${\mathrm{Ke}}^2/5\mathrm{r}$

${10}^3$ 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.  $8\times {10}^{-15} \mathrm{m}$

Calculate the area of the plates of a one farad parallel plate capacitor if the separation between plates is $1 \mathrm{mm}$ and plates are in a vacuum.

1.  $18\times {10}^8 {\mathrm{m}}^2$                 

2.  $0.3\times {10}^8 {\mathrm{m}}^2$

3.  $1.3\times {10}^8 {\mathrm{m}}^2$               

4.  $1.13\times {10}^8 {\mathrm{m}}^2$

A solid conducting sphere of radius a having a charge $\mathrm{q}$ is surrounded by a concentric conducting spherical shell of inner radius $2\mathrm{a}$ and outer radius $3\mathrm{a}$ as shown in figure.

Find the amount of heat produced when switch is closed.

1. ${\mathrm{Kq}}^2/2\mathrm{a}$                         

2. ${\mathrm{Kq}}^2/3\mathrm{a}$

3. ${\mathrm{Kq}}^2/4\mathrm{a}$                         

4. ${\mathrm{Kq}}^2/6\mathrm{a}$

Three uncharged capacitors of capacities \(C_1, C_2~\text{and}~C_3\) are connected to one another as shown in the figure.

If points A, B, and D, are at potential \(V_1, V_2 ~\text{and}~V_3\) then the potential at O will be:

A parallel plate capacitor of area ‘A’ , plate separation ‘d’ is filled with two dielectrics as shown. What is the capacitance of the arrangement ?

1.  $\frac{3{\mathrm{K\epsilon }}_0\mathrm{A}}{4\mathrm{d}}$                             

2. $\frac{4{\mathrm{K\epsilon }}_0\mathrm{A}}{3\mathrm{d}}$

3. $\frac{\left(\mathrm{K}+1\right){\mathrm{\epsilon }}_0\mathrm{A}}{2\mathrm{d}}$                       

4.$\frac{\mathrm{K}\left(\mathrm{K}+3\right){\mathrm{\epsilon }}_0\mathrm{A}}{2\left(\mathrm{K}+1\right)\mathrm{d}}$