Draw graphs showing the variations of the electric field and potential due to a uniformly charged sphere with distance from its centre.

(i) at a point near an infinitely large uniformly charged line charge. Explain why an infinite length is necessary for the result.

(ii) at a point near an infinitely large uniformly charged cylinder.

(c) the length of the surface is parallel to $Y$-axis, but the normal drawn to it is inclined to the $X$ -axis at an angle of ${60}^{°}$.

An uncharged square metal plate with side $2 \mathrm{m}$ is placed in a uniform field of magnitude $5\times {10}^5 {\mathrm{NC}}^{-1}$ at right angle to the direction of the field. Find

the corresponding electric fields.

Three concentric spherical metallic shells $A,B$ and $C$ of radii $a,b$ and $c(a<b<c)$ have surface charge densities $\sigma ,-\sigma$ and $\sigma$ respectively. If the shells $A$ and $C$ are at the same potential, obtain the relation between the radii $a,b$ and $c.$