Draw a graph showing variation of potential with $r$ distance for a uniformly charged spherical shell.

Ten charges are placed on the circumference of a circle of radius $R$ with constant angular separation between successive charges. Alternate charges $1,3,5,7,9$ have charge $(+q)$ each, while $2,4,6,8,10$ have charge $(-q)$ each. The potential $V$ and the electric field $E$ at the centre of the circle are respectively

(Take $V =0$ at infinity $)$

A charge $+q$ is distributed over a thin ring of radius $r$ with line charge density $\lambda=q \sin ^{2} \theta /(\pi r)$. Note that the ring is in the $X Y$ - plane and $\theta$ is the angle made by $r$ with the $X$-axis. The work done by the electric force in displacing a point charge $+ Q$ from the centre of the ring to infinity is

The electric field $\vec E$ between two points is constant in both magnitude and direction. Consider a path of length d at an angle $\theta = 60^o$ with respect to field lines shown in figure. The potential difference between points $1$ and $2$ is

Equal charges are given to two spheres of different radii. The potential will

Two electric charges $12\,\mu C$ and $ - 6\,\mu C$ are placed $20\, cm$ apart in air. There will be a point $P$ on the line joining these charges and outside the region between them, at which the electric potential is zero. The distance of $P$ from $ - 6\,\mu C$ charge is.......$m$