Three concentric spherical shells have radii a, b and c (a<b<c) and have surface charge densities $\mathrm{\sigma }, -\mathrm{\sigma }$ and $\mathrm{\sigma }$ respectively. If ${\mathrm{V}}_{\mathrm{A}}, {\mathrm{V}}_{\mathrm{B}}$ and ${\mathrm{V}}_{\mathrm{C}}$ denote the potential of the three shells, if c=a+b, we have

(1) ${\mathrm{V}}_{\mathrm{C}}={\mathrm{V}}_{\mathrm{A}}\ne {\mathrm{V}}_{\mathrm{B}}$                                       

(2) ${\mathrm{V}}_{\mathrm{C}}={\mathrm{V}}_B\ne {\mathrm{V}}_{\mathrm{A}}$

(3) ${\mathrm{V}}_{\mathrm{C}}\ne {\mathrm{V}}_B\ne {\mathrm{V}}_A$                                       

(4) ${\mathrm{V}}_{\mathrm{C}}={\mathrm{V}}_B={\mathrm{V}}_A$

A parallel plate air capacitor has a capacity of C, the distance of separation between plates is d and potential difference V is applied between the plates. The force of attraction between the plates of the parallel plate air capacitor is:

1. $\frac{C^2{V}^2}{2d}$

2. $\frac{C{V}^2}{2d}$

3. $\frac{C{V}^2}{d}$

4. $\frac{C^2{V}^2}{2d^2}$

The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is

1. Independent of the distance between the plates

2. linearly proportional to the distance between the plates

3. proportional to the sqaure root of the distance between the plates

4. inversely proportional to the distance between the plates

Charges +q and –q are placed at points A and B, respectively; which are at a distance 2L apart, C is the midpoint between A and B. The work done in moving a charge +Q along the semicircle CRD is : 
`

1. $\frac{qQ}{4{\mathrm{\pi \epsilon }}_0\mathrm{L}}$

2. $\frac{qQ}{2{\mathrm{\pi \epsilon }}_0\mathrm{L}}$

3. $\frac{qQ}{6{\mathrm{\pi \epsilon }}_0\mathrm{L}}$

4. $-\frac{qQ}{6{\mathrm{\pi \epsilon }}_0\mathrm{L}}$

A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with four dielectric materials having dielectric constants k₁, k₂, k₃ and k₄ as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by 

1.  $\mathrm{K}={\mathrm{k}}_1+{\mathrm{k}}_2+{\mathrm{k}}_3+3{\mathrm{k}}_4$

2.  $\mathrm{k}=\frac{2}{3}{\mathrm{k}}_4\left(\frac{{\mathrm{k}}_1}{{\mathrm{k}}_1+{\mathrm{K}}_4}+\frac{{\mathrm{k}}_2}{{\mathrm{k}}_2+{\mathrm{k}}_4}+\frac{{\mathrm{k}}_3}{{\mathrm{k}}_3+{\mathrm{k}}_4}\right)$

3.  $\frac{2}{\mathrm{k}}=\frac{3}{{\mathrm{k}}_1+{\mathrm{k}}_2+{\mathrm{k}}_3}+\frac{1}{{\mathrm{k}}_4}$

4.  $\frac{1}{\mathrm{k}}=\frac{1}{{\mathrm{k}}_1}+\frac{1}{{\mathrm{k}}_2}+\frac{1}{{\mathrm{k}}_3}+\frac{3}{2{\mathrm{k}}_4}$

A series combination of n1 capacitors, each of value C₁, is charged by a source of potential difference 4V. When another parallel combination of n₂ capacitors, each of value C₂, is charged by a source of potential difference V, it has the same (total) energy stored in it, as the first combination has. The value of C₂ , in terms of C₁, is then

1. $\frac{2C_1}{n_1{n}_2}$

2. $16\frac{n_2}{n_1}{C}_1$

3. $2\frac{n_2}{n_1}{C}_1$

4. $\frac{16C_1}{n_1{n}_2}$

Four point charges –Q, -q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the center of the square is zero, is

1. Q=-q

2. Q= -2q

3. Q=q

4. Q=2q

A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere respectively are:

1. Zero and $\frac{Q}{4{\mathrm{\pi \epsilon }}_0{\mathrm{R}}^2}$

2. $\frac{Q}{4{\mathrm{\pi \epsilon }}_0\mathrm{R}}$ and zero

3. $\frac{Q}{4{\mathrm{\pi \epsilon }}_0\mathrm{R}}$ and $\frac{Q}{4{\mathrm{\pi \epsilon }}_0{\mathrm{R}}^2}$

4. Both are zero.