Two concentric hollow conducting spheres of radius r and R are shown. The charge on the outer shell is Q. What charge should be given to the inner sphere so that the potential at any point P outside the outer sphere is zero?

1. $-\frac{\mathrm{Qr}}{\mathrm{R}}$

2. $-\frac{\mathrm{QR}}{\mathrm{r}}$

3. $-\mathrm{Q}$

4. $-\frac{2\mathrm{QR}}{\mathrm{r}}$

The potential gradient is a:
1. vector quantity.
2. scalar quantity.
3. conversion factor.
4. constant.

The electric potential V at a point P(x, y, z) in space is given by $\mathrm{V}=4{\mathrm{x}}^2$ volt. The electric field at a point (1m, 0, 2m) in V/m is:

1. 8 along the -ve x-axis

2. 8 along the +ve x-axis

3. 16 along the -ve x-axis

4. 16 along the +ve x-axis

The figure shows the variation of electric field intensity E with distance x. What is the potential difference between two points at x=2 m and at x=6 m from O?

 
1. 30 V
2. 60 V
3. 40 V
4. 80 V

The figure shows a set of equipotential surfaces. The magnitude and direction of the electric field that exists in the region are:

1. $10\sqrt{2}$ V/m at $45°$ with x-axis

2. $10\sqrt{2}$ V/m at $-45°$ with x-axis

3. $5\sqrt{2}$ V/m at $45°$ with x-axis

4. $5\sqrt{2}$ V/m at $-45°$ with x-axis

Determine the electric field strength vector if the potential of this field depends on x, y coordinates as V=10axy.

1. $10 \mathrm{a} (\mathrm{y}\hat{\mathrm{i}}+\mathrm{x}\hat{\mathrm{j}})$

2. $-10 \mathrm{a} (\mathrm{y}\hat{\mathrm{i}}+\mathrm{x}\hat{\mathrm{j}})$

3. $-\mathrm{a} (\mathrm{y}\hat{\mathrm{i}}+\mathrm{x}\hat{\mathrm{j}})$

4. $-10 \mathrm{a} (\mathrm{x}\hat{\mathrm{i}}+\mathrm{y}\hat{\mathrm{k}})$

If on the x-axis, the electric potential decreases uniformly from 60 V to 20 V between x=-2 m to x=+2 m, then the magnitude of electric field at the origin:

1. must be 10 V/m.

2. may be greater than 10 V/m.

3. is zero.

4. is 5 V/m.

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