A dipole with two electric charges of 2 $$\mu$$C magnitude each, with separation distance 0.5 $$\mu$$m, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by 30° from the axis, the value of the torque is :

Magnitude of each charge of the dipole: $$q = 2\,\mu C = 2 \times 10^{-6}\,C$$.

Separation of the charges (length of dipole): $$d = 0.5\,\mu m = 0.5 \times 10^{-6}\,m$$.

Electric dipole moment is defined as $$p = q\,d$$ (directed from -ve to +ve charge).

Substituting the values,
$$p = (2 \times 10^{-6}) \times (0.5 \times 10^{-6})$$
$$p = 1 \times 10^{-12}\,C\,m$$.

The electric field E between parallel-plate capacitor plates is uniform and given by $$E = \frac{V}{\ell}$$, where V is the applied potential difference and $$\ell$$ is plate separation.

Given potential difference: $$V = 5\,V$$.
Plate separation: $$\ell = 0.5\,mm = 0.5 \times 10^{-3}\,m$$.

Therefore,
$$E = \frac{5}{0.5 \times 10^{-3}} = \frac{5}{5 \times 10^{-4}} = 1 \times 10^{4}\,V\,m^{-1}$$.

Torque on a dipole in a uniform field is $$\tau = p\,E\,\sin\theta$$, where $$\theta$$ is the angle between $$\vec p$$ and $$\vec E$$ after rotation.

The dipole is rotated through $$30^{\circ}$$, so $$\theta = 30^{\circ}$$ and $$\sin30^{\circ} = 0.5$$.

Hence,
$$\tau = (1 \times 10^{-12})(1 \times 10^{4})(0.5)$$
$$\tau = 0.5 \times 10^{-8}\,N\,m$$
$$\tau = 5 \times 10^{-9}\,N\,m$$.

Therefore the torque experienced by the dipole is $$5 \times 10^{-9}\,N\,m$$.

Option A is correct.