A point charge Q is placed at a distance d from the centre of an uncharged conducting sphere of radius R. The potential of the sphere is (d > R) –

1. $\frac{1}{4\mathrm{\pi } {\in }_0}.\frac{\mathrm{Q}}{\left(\mathrm{d}-\mathrm{R}\right)}$                     

2. $\frac{1}{4\mathrm{\pi } {\in }_0}.\frac{\mathrm{Q}}{\mathrm{d}}$

3. $\frac{1}{4\mathrm{\pi } {\in }_0}.\frac{\mathrm{Q}}{\mathrm{R}}$                             

4. zero

Two identical capacitors are joined in parallel, charged to a potential V and then separated and then connected in series i.e. the positive plate of one is connected to negative of the other 

(1) The charges on the free plates connected together are destroyed

(2) The charges on the free plates are enhanced

(3) The energy stored in the system increases

(4) The potential difference in the free plates becomes 2V

Figure shows an electric line of force which curves along a circular arc.

The magnitude of electric field intensity is same at all points on this curve and is equal to E. If the potential at A is V, then the potential at B is –

1. $\mathrm{V}-\mathrm{ER\theta }$                             

2. $\mathrm{V}-2\mathrm{ER} \sin \frac{\mathrm{\theta }}{2}$

3. $\mathrm{V}+\mathrm{ER\theta }$                             

4. $\mathrm{V}+2\mathrm{ER} \sin \frac{\mathrm{\theta }}{2}$

If W be the amount of heat produced in the process of charging an uncharged capacitor then the amount of energy stored in it is

(1) 2W

(2) $\frac{W}{2}$

(3) W

(4) zero

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.  ${\mathrm{Ke}}^2/5\mathrm{r}$

Two identical point charges are placed at a separation of d. P is a point on the line joining the charges, at a distance x from any one charge. The field at P is E, E is plotted against x for values of x from close to zero to slightly less than d. Which of the following represents the resulting curve?

(1)

(2)

(3)

(4)

A capacitor of $1 \mu \mathrm{F}$ withstands a maximum voltage of 6 kilovolt while another capacitor of $2 \mu \mathrm{F}$ withstands a maximum voltage of 4 kilovolt. If the two capacitors are connected in series, the system will withstand a maximum voltage of –

1.  2 kV                 

2.  4 kV 

3.  6 kV                 

4.  9 kV

The figure shows some of the equipotential surfaces. The magnitude and direction of the electric field are given by:

An air capacitor of capacity $C=10\mu F$ is connected to a constant voltage battery of 12 V. Now the space between the plates is filled with a liquid of dielectric constant 5. The charge that flows now from battery to the capacitor is

(1) 120 $\mu C$

(2) 699 $\mu C$

(3) 480 $\mu C$

(4) 24 $\mu C$

The variation of potential with distance R from a fixed point is as shown below. The electric field at R = 5 m is 

(1) 2.5 volt/m

(2) –2.5 volt/m

(3) 2/5 volt/m

(4) –2/5 volt/m