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 square root of the distance between the plates
4.	inversely proportional to the distance between the plates

Maximum charge stored on a metal sphere of radius 15 cm may be $7.5$ $\mathrm{\mu C}$. The potential energy of the sphere in this case is:
1. 9.67 J
2. 0.25 J
3. 3.25 J
4. 1.69 J

Four electric charges \(+\mathrm q,\) \(+\mathrm q,\) \(-\mathrm q\) and \(-\mathrm q\) are placed at the corners of a square of side \(2\mathrm{L}\) (see figure). The electric potential at point A, mid-way between the two charges \(+\mathrm q\) and \(+\mathrm q\) is:
              

1.  $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{2\mathrm{q}}{\mathrm{L}}\left(1+\frac{1}{\sqrt{5}}\right)$

2.  $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{2\mathrm{q}}{\mathrm{L}}\left(1-\frac{1}{\sqrt{5}}\right)$

3.  zero

4.  $\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{2\mathrm{q}}{\mathrm{L}}\left(1+\sqrt{5}\right)$

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, and c=a+b, it can be concluded that:

The electric potential at a point in free space due to a charge \(Q\) coulomb is \(Q\times10^{11}~\text{V}\). The electric field at that point is:
1. \(4\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)
2. \(12\pi \varepsilon_0 Q\times 10^{20}~\text{V/m}\)
3. \(4\pi \varepsilon_0 Q\times 10^{20}~\text{V/m}\)
4. \(12\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)

Two condensers, one of capacity \(C\) and the other of capacity \(\frac{C}2\) are connected to a \(V\) volt battery, as shown in the figure. 
          
The energy stored in the capacitors when both condensers are fully charged will be:
1. \(2CV^2\)
2. \({1 \over4}CV^2\)
3. \({3 \over4}CV^2\)
4. \({1 \over2}CV^2\)

An electric dipole of moment \(\vec {p} \) is lying along a uniform electric field \(\vec{E}\). The work done in rotating the dipole by \(90^{\circ}\) is:
1. \(\sqrt{2}pE\)
2. \(\frac{pE}{2}\)
3. \(2pE\)
4. \(pE\)

An electric dipole with dipole moment $\overrightarrow{\mathrm{p}}=\left(3\hat{i}+4\hat{j}\right)\times {10}^{-30}$ $C-\mathrm{m }$is placed in an electric field $\overrightarrow{\mathrm{E}}=4000\hat{i}\left(N/C\right)$. An external agent turns the dipole slowly until its electric dipole moment becomes $\left(-4\hat{i}+3\hat{j}\right)\times {10}^{-30}$ $C-m$. The work done by the external agent is equal to:

1. 4 × 10^–28  J 

2. –4 × 10^–28  J

3. 2.8 × 10^–26  J 

4. –2.8 × 10^–26  J

The variation of potential with distance x from a fixed point is shown in the figure. The electric field at x =13 m is:

1. 7.5 volt/meter 

2. –7.5 volt/meter

3. 5 volt/meter 

4. –5 volt/meter

In the circuit diagram shown all the capacitors are in  \(\mu F\).  The equivalent capacitance between points, A & B is (in $\mathrm{\mu }$F):

1. 14/5 

2. 7.5

3. 3/7 

4. None of these