An infinite conducting sheet has a surface charge density $\mathrm{\sigma }$. The distance between the two equipotential surface is r. The potential difference between these two surfaces is:

1. $\frac{\mathrm{\sigma r}}{2{\mathrm{\epsilon }}_0}$

2. $\frac{\mathrm{\sigma r}}{{\mathrm{\epsilon }}_0}$

3. $\frac{\mathrm{\sigma }}{{\mathrm{\epsilon }}_0\mathrm{r}}$

4. $\frac{\mathrm{\sigma }}{2{\mathrm{\epsilon }}_0\mathrm{r}}$

Two small spheres each carrying a charge q are placed at distance r apart. If one of the spheres is taken around the other in a circular path, the work done will be equal to:

1. Force between them $\times$ r

2. $\frac{\mathrm{Force} \mathrm{between} \mathrm{them}}{2\mathrm{\pi r}}$

3. Force between them $\times 2\mathrm{\pi r}$

4. Zero

Work done in moving a charge q coulomb on the surface of a given charged conductor of potential V is:

1. $\frac{\mathrm{V}}{\mathrm{q}}$ joule

2. $\mathrm{Vq}$ joule

3. $\frac{\mathrm{q}}{\mathrm{V}}$ joule

4. Zero

If an $\mathrm{\alpha }$-particle and a proton are accelerated from rest by a potential difference of 1 megavolt, then the ratio of their kinetic energies will be:

1. $\frac{1}{2}$

2. 1

3. 2

4. 4

Three charges -q, Q and -q are placed respectively at equal distances on a straight line. If the potential energy of the system of three charges is zero, then what is the ratio of Q:q?

1. 1: 1

2. 1: 2

3. 1: 3

4. 1: 4

A particle A has charge +q and another particle B has charge +4q with each of them having the same mass m. When allowed to fall from rest through the same electric potential difference, the ratio of their speeds $\frac{{\mathrm{v}}_{\mathrm{A}}}{{\mathrm{v}}_{\mathrm{B}}}$ will become:

1. 1: 2

2. 2: 1

3. 1: 4

4. 4: 1

If \(50~\text{J}\) of work must be done to move an electric charge of \(2~\text{C}\) from a point where the potential is \(-10~\text {volts}\) to another point where the potential is \(\text{V volts}\), then the value of \(\mathrm{V}\) is:
1. \(5~\text {volts}\)
2. \(-15~\text {volts}\)
3. \(+15~\text {volts}\)
4. \(+10~\text {volts}\)

A proton has a mass $1.67\times {10}^{-27}$ kg and a charge $+1.6\times {10}^{-19}$ C. If the proton is accelerated through a potential difference of 1 million volts, then the kinetic energy is:

1. $1.6\times {10}^{-15} \mathrm{J}$

2. $1.6\times {10}^{-13} \mathrm{J}$

3. $1.6\times {10}^{-21} \mathrm{J}$

4. $3.2\times {10}^{-13} \mathrm{J}$

Calculate the work done in taking a charge $-2\times {10}^{-9}$ C from A to B via C. (in the diagram)

1. 0.2 joule

2. 1.2 joule

3. 2.2 joule

4. Zero

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