Two conducting hollow spheres of radii $R$ and $3R$ are found to have $Q$ charge on their outer surfaces when both are connected with a long wire. $A$ charge $q'$ is kept at the centre of the bigger sphere. Which of the following is true?

$A$ hollow metal sphere of radius $10 \ cm$ is charged such that the potential on its surface becomes $80 \ V$. The potential at the centre of the sphere is . . . . . . . (in $V$)

Three concentric metal shells $A, B$ and $C$ of respective radii $a, b$ and $c$ $(a < b < c)$ have surface charge densities $+\sigma, -\sigma$ and $+\sigma$ respectively. The potential of shell $B$ is

Four identical charges $+50\,\mu C$ each are placed,one at each corner of a square of side $2\,m$. How much external energy is required to bring another charge of $+50\,\mu C$ from infinity to the centre of the square? (Given $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\,\frac{N\cdot m^2}{C^2}$)

Which of the following graphs correctly shows how the electrostatic potential $V$ varies with distance $r$ from a point charge?

$A$ non-conducting ring of radius $0.5\,m$ carries a total charge of $1.11 \times 10^{-10}\,C$ distributed non-uniformly on its circumference,producing an electric field $\vec{E}$ everywhere in space. The value of the line integral $\int_{l = \infty }^{l = 0} { - \vec{E} \cdot d\vec{l} }$ (where $l = 0$ is the centre of the ring) in volts is: