Appeared in: 2025 (2 sets)
(a) (i) The electric field in a region is given by $\vec{E} = 40x\hat{i}\text{ N/C}$. Find the amount of work done in taking a unit positive charge from a point $(0, 3\text{m})$ to the point $(5\text{m}, 0)$.
(ii) A charge $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R$ ($> r$) such that their surface charge densities are equal. Find :
(I) the electric field, and
(II) the potential
at their common centre.