A dipole with two electric charges of $2\ \mu\text{C}$ magnitude each, with separation distance $0.5\ \mu\text{m}$, is placed between the plates of a capacitor such that its axis is parallel to the electric field established between the plates when a potential difference of $5\ \text{V}$ is applied. The separation between the plates is $0.5\ \text{mm}$. If the dipole is rotated by $30^\circ$ from the axis, it tends to realign in the direction due to a torque. The value of the torque is:
Answer: (A) $5\times10^{-9}\ \text{N m}$
$E = \dfrac Vd = \dfrac{5}{0.5\times10^{-3}} = 10^4\ \text{V/m}$ and $p = qa = 2\times10^{-6}\times0.5\times10^{-6} = 10^{-12}\ \text{C m}$.
$$\tau = pE\sin30^\circ = 10^{-12}\times10^4\times\frac12 = 5\times10^{-9}\ \text{N m}$$
Solution by Sreeraj P, M.Sc Physics