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

A charge +q is fixed at each of the points $\mathrm{x}={\mathrm{x}}_0, \mathrm{x}=3{\mathrm{x}}_0, \mathrm{x}=5{\mathrm{x}}_0$, ........... upto $\infty$ on X-axis and charge –q is fixed on each of the points $\mathrm{x}=2{\mathrm{x}}_0, \mathrm{x}=4{\mathrm{x}}_0, \mathrm{x}=6{\mathrm{x}}_0$,............. upto $\infty$. Here ${\mathrm{x}}_0$ is a positive constant. Take the potential at a point due to a charge Q at a distance r from it to be $\frac{\mathrm{Q}}{4{\mathrm{\pi \epsilon }}_0\mathrm{r}}$. Then the potential at the origin due to above system of charges will be

1. zero                           

2. $\frac{\mathrm{q}}{8{\mathrm{\pi \epsilon }}_0{\mathrm{x}}_0 {\log }_{\mathrm{e}} 2}$

3. $\infty$                             

4. $\frac{\mathrm{q} {\log }_{\mathrm{e}} 2}{4{\mathrm{\pi \epsilon }}_0{\mathrm{x}}_0}$

A parallel plate capacitor of capacitance C is connected to a battery and is charged to a potential difference V. Another capacitor of capacitance 2C is connected to another battery and is charged to potential difference 2V. The charging batteries are now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is 

(1) Zero

(2) $\frac{25C{V}^2}{6}$

(3) $\frac{3C{V}^2}{2}$

(4) $\frac{9C{V}^2}{2}$

The electric potential at a point (x, y) in the x – y plane is given by V = –kxy. The field intensity at a distance r from the origin varies as 

(1) r²

(2) r

(3) $\frac{1}{r}$

(4) $\frac{1}{r^2}$

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