A thin half ring of radius $R$ is uniformly charged with a total charge $Q$. What is the magnitude of the electric field at the centre of curvature of the half ring?
A thin non-conducting rod has charge $Q$ and a length $a$. The charge is spread uniformly along the rod. Find the electric field at a point at a $P$ distance $r$ from the rod, along the perpendicular bisector.
A thin, non-conducting ring of radius $r$ has a charge $Q$ placed on it. Find the electric field at a point $P$ on the axis at a distance $x$ from the centre of the ring. At what value of $x$ is the field the maximum?
A hollow spherical shell of inner radius $r_{1}$ and outer radius $r_{2}$ carries a charge density $\rho=k / r^{2}$. Find the electric field for $r<r_{1}, r_{1}<r<r_{2}$ and $r>r_{2}$.
A small sphere of mass $m$ with a charge $q$ hangs from a thread which makes an angle $\theta$ with a large, conducting charged plate. Find the charge density of the plate.
