Two electrons are moving towards each other, each with a velocity of ${10}^6$ m/s. What will be the closest distance of approach between them?

1. $1.53\times {10}^{-8} \mathrm{m}$

2. $2.53\times {10}^{-10} \mathrm{m}$

3. $3.53\times {10}^{-6} \mathrm{m}$

4. Zero

A point charge q is surrounded by eight identical charges at distance r as shown in the figure. How much work is done by the forces of electrostatic repulsion when the point charge at the centre is removed to infinity?

1. Zero

2. $\frac{8{\mathrm{q}}^2}{4{\mathrm{\pi \epsilon }}_0\mathrm{r}}$

3. $\frac{8\mathrm{q}}{4{\mathrm{\pi \epsilon }}_0\mathrm{r}}$

4. $\frac{64{\mathrm{q}}^2}{4{\mathrm{\pi \epsilon }}_0\mathrm{r}}$

1000 small water drops, each of capacitance C, join together to form one large spherical drop. The capacitance of the bigger sphere is:

1. C

2. 10C

3. 100C

4. 1000C

Two similar conducting balls having charges +q and -q are placed at a separation d from each other in the air. The radius of each ball is r and the separation between their centres is d(d>>r). Calculate the capacitance of the two-ball system.

1. $4{\mathrm{\pi \epsilon }}_0\mathrm{r}$

2. $2{\mathrm{\pi \epsilon }}_0\mathrm{r}$

3. $4{\mathrm{\pi log}}_{\mathrm{e}}\frac{{\mathrm{\epsilon }}_0\mathrm{r}}{\mathrm{d}}$

4. $4{\mathrm{\pi log}}_{\mathrm{e}}\frac{\mathrm{r}}{\mathrm{d}}$

Two parallel plate capacitors have their plate areas 100 cm² and 500 cm² respectively. If they have the same charge and potential and the distance between the plates of the first capacitor is 0.5 mm, then the distance between the plates of the second capacitor is:

1. 0.10 cm

2. 0.15 cm

3. 0.20 cm

4. 0.25 cm

A dielectric slab of dielectric constant K is placed between the plates of a parallel plate capacitor carrying charge q. The induced charge q' on the surface of the slab is given by:

1. $\mathrm{q}\text{'}=\mathrm{q}-\frac{\mathrm{q}}{\mathrm{K}}$

2. $\mathrm{q}\text{'}=-\mathrm{q}+\frac{\mathrm{q}}{\mathrm{K}}$

3. $\mathrm{q}\text{'}=\mathrm{q}\left[\frac{1}{\mathrm{K}}+1\right]$

4. $\mathrm{q}\text{'}=-\mathrm{q}\left(1+\frac{1}{\mathrm{K}}\right)$

Two charge capacitors have their outer plates fixed and inner plates connected by a spring of force constant 'k'. The charge on each capacitor is q. Find the extension in the spring at equilibrium

1. $\frac{{\mathrm{q}}^2}{2{\mathrm{A\epsilon }}_0\mathrm{k}}$

2. $\frac{{\mathrm{q}}^2}{4{\mathrm{A\epsilon }}_0\mathrm{k}}$

3. $\frac{{\mathrm{q}}^2}{{\mathrm{A\epsilon }}_0\mathrm{k}}$

4. Zero

The following arrangement consists of five identical metal plates parallel to each other. The area of such plate is A and separation between the successive plates is d. The capacitance between P and Q is:

1. $\frac{5{\mathrm{\epsilon }}_0\mathrm{A}}{\mathrm{d}}$

2. $\frac{7}{3}{\mathrm{\epsilon }}_0\frac{\mathrm{A}}{\mathrm{d}}$

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

4. $\frac{5}{3}\frac{{\mathrm{\epsilon }}_0\mathrm{A}}{\mathrm{d}}$

A capacitor is half-filled with a dielectric (K=2) as shown in figure A. If the same capacitor is to be filled with the same dielectric as shown in figure B, what would be the thickness of the dielectric so that the capacitor still has the same capacity?

1. 2d/3

2. 3d/2

3. 3d/4

4. 4d/3

Capacitors ${\mathrm{C}}_1\left(10\mathrm{\mu F}\right)$ and ${\mathrm{C}}_2\left(20\mathrm{\mu F}\right)$ are connected in series across a 3 kV supply as shown. What is the charge on the capacitor C₁?

1. $45000 \mathrm{\mu C}$

2. $20000 \mathrm{\mu C}$

3. $15000 \mathrm{\mu C}$

4. $10000 \mathrm{\mu C}$