Two small spherical balls of mass $10\ \text{g}$ each with charges $-2\ \mu\text{C}$ and $2\ \mu\text{C}$ are attached to the two ends of a very light rigid rod of length $20\ \text{cm}$. The arrangement is now placed near an infinite non-conducting charge sheet with uniform charge density of $100\ \mu\text{C/m}^2$ such that the length of the rod makes an angle of $30^\circ$ with the electric field generated by the charge sheet. The net torque acting on the rod is: (Take $\varepsilon_0 = 8.85\times10^{-12}\ \text{C}^2/\text{N m}^2$)
Answer: (B) $1.12\ \text{N m}$
The rod with its charges is a dipole of moment $p = qd = 2\times10^{-6}\times0.2 = 4\times10^{-7}\ \text{C m}$, in a uniform field
$$E = \frac{\sigma}{2\varepsilon_0} = \frac{100\times10^{-6}}{2\times8.85\times10^{-12}} = 5.65\times10^6\ \text{N/C}$$
$$\tau = pE\sin30^\circ = 4\times10^{-7}\times5.65\times10^6\times\frac12 \approx 1.13\ \text{N m}$$
This matches $1.12\ \text{N m}$ (the difference is rounding).
Solution by Sreeraj P, M.Sc Physics