A hollow metal sphere of radius $5\, cm$ is charged so that the potential on its surface is $10\, V$. The potential at the centre of the sphere is

Assertion : For a non-uniformly charged thin circular ring with net charge is zero, the electric field at any point on axis of the ring is zero.

Reason : For a non-uniformly charged thin circular ring with net charge zero, the electric potential at each point on axis of the ring is zero.

$STATEMENT-1$ For practical purposes, the earth is used as a reference at zero potential in electrical circuits.and

$STATEMENT-2$ The electrical potential of a sphere of radius $R$ with charge $\mathrm{Q}$ uniformly distributed on the surface is given by $\frac{\mathrm{Q}}{4 \pi \varepsilon_0 R}$.

Derive an expression for the electric potential in a electric field of positive point charge at distance $\mathrm{r}$.

The give graph shown variation (with distance $r$ from centre) of

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