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

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. \(pE\)

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. \(12\pi \varepsilon_0 Q\times 10^{22}~\text{V/m}\)

The figure shows some of the equipotential surfaces. Magnitude and direction of the electric field is given by:

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

In the given figure if $\mathrm{V}=4 v\mathrm{olt}$, each plate of the capacitor has a surface area of ${10}^{-\mathrm{2 }}{\mathrm{m}}^2$ and the plates are $0.1\times {10}^{-\mathrm{3 }}\mathrm{m}$ apart, then the number of excess electrons on the negative plate is:

1. $5.15\times {10}^9$

2. $2.21\times {10}^{10}$

3. $3.33\times {10}^9$

4. $2.21\times {10}^9$

Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p. If P is a point at a distance r from the centre of the dipole and the line joining the centre of the dipole to this point makes an angle θ with the axis of the dipole, then the potential at P is given by: (r >> 2a) (Where p = 2qa) 

Two thin dielectric slabs of dielectric constants K₁&K₂ ($K_1<K_2$) are inserted between plates of a parallel capacitor, as shown in the figure. The variation of electric field E between the plates with distance d as measured from plate P is correctly shown by:  
  

1.		2.
3.		4.

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

An electric dipole of moment \(p\) is placed in an electric field of intensity \(E\). The dipole acquires a position such that the axis of the dipole makes an angle \(\theta\) with the direction of the field. Assuming that the potential energy of the dipole to be zero when \(\theta = 90^{\circ},\) the torque and the potential energy of the dipole will respectively be: