(a) (i) A small conducting sphere A of radius $r$ charged to a potential $V$, is enclosed by a spherical conducting shell B of radius $R$. If A and B are connected by a thin wire, calculate the final potential on sphere A and shell B. (ii) Write two characteristics of equipotential surfaces. A uniform electric field of $50 \text{ NC}^{-1}$ is set up in a region along $+x$ axis. If the potential at the origin $(0, 0)$ is $220 \text{ V}$, find the potential at a point $(4\text{m}, 3\text{m})$. OR (b) (i) What is difference between an open surface and a closed surface ? Draw elementary surface vector $d\vec{S}$ for a spherical surface $S$. (ii) Define electric flux through a surface. Give the significance of a Gaussian surface. A charge outside a Gaussian surface does not contribute to total electric flux through the surface. Why ? (iii) A small spherical shell $S_1$ has point charges $q_1 = -3 \text{ }\mu\text{C}$, $q_2 = -2 \text{ }\mu\text{C}$ and $q_3 = 9 \text{ }\mu\text{C}$ inside it. This shell is enclosed by another big spherical shell $S_2$. A point charge $Q$ is placed in between the two surfaces $S_1$ and $S_2$. If the electric flux through the surface $S_2$ is four times the flux through surface $S_1$, find charge $Q$.