A charge $Q$ is distributed over two concentric hollow spheres or radius $r$ and $R(> r)$ such that the surface densities are equal. The potential at the common centre is
$\frac{{Q\left( {{R^2} + {r^2}} \right)}}{{4\pi {\varepsilon _0}\left( {R + r} \right)}}$
$\frac{Q}{{R + r}}$
Zero
$\frac{{Q\left( {R + r} \right)}}{{4\pi {\varepsilon _0}\left( {{R^2} + {r^2}} \right)}}$
Charges $+q$ and $-q$ are placed at points $A$ and $B$ respectively which are at distance $2\,L$ apart, $C$ is the midpoint between $A$ and $B$ . The work done in moving a charge $+ Q$ along the semicircle $CRD$ is
Two condensers, one of capacity $C$ and the other of capacity $\frac{C}{2}$ , are connected to a $V\, volt$ battery, as shown. The work done in charging fully both the condensers is
A thin spherical conducting shell of radius $R$ has a charge $q.$ Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at a point $p$ a distance $R/2$ from the centre of the shell is
A $2\,\mu F$ capacitor is charged as shown in the figure. The percentage of its stored energy dissipated after the switch $S$ is turned to position $2$, is.....$\%$
Two spherical conductors $A$ and $B$ of radii $1\, mm$ and $2\, mm$ are separated by a distance of $5\, cm$ and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres $A$ and $B$ is-