Three particles, each of mass $1 \mathrm{g}$ and carrying a charge $q$, are suspended from a common point by insulated massless strings, each $100 \mathrm{cm}$ long. The particles are in equilibrium and are located at the corners of an equilateral triangle of side length $3 \mathrm{cm}$, if the charge $q$ on each particle is $n\times {10}^{-9} \mathrm{C}$. Find the value of $n$ (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$).

The figure shows three infinite non-conducting plates of charge perpendicular to the plane of the paper with charge per unit area $+\sigma ,+2\sigma$ and $-\sigma$. Find the ratio of the net electric field at that point $A$ to that at point $B$.

In the figure shown $S$ is a large nonconducting sheet of uniform charge density $\sigma . A$ rod $R$ of length $\ell$ and mass '$m$' is parallel to the sheet and hinged at its mid point. The linear charge densities on the upper and lower half of the rod are shown in the figure. If the angular acceleration of the rod just after it is released is $\frac{x\sigma \lambda }{2m{\epsilon }_0}$, then find the value of $x$.