Consider two charged metallic spheres $S_{1}$ and $\mathrm{S}_{2}$ of radii $\mathrm{R}_{1}$ and $\mathrm{R}_{2},$ respectively. The electric $\left.\text { fields }\left.\mathrm{E}_{1} \text { (on } \mathrm{S}_{1}\right) \text { and } \mathrm{E}_{2} \text { (on } \mathrm{S}_{2}\right)$ on their surfaces are such that $\mathrm{E}_{1} / \mathrm{E}_{2}=\mathrm{R}_{1} / \mathrm{R}_{2} .$ Then the ratio $\left.\mathrm{V}_{1}\left(\mathrm{on}\; \mathrm{S}_{1}\right) / \mathrm{V}_{2} \text { (on } \mathrm{S}_{2}\right)$ of the electrostatic potentials on each sphere is
$\left(\frac{\mathrm{R}_{2}}{\mathrm{R}_{1}}\right)$
$\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{3}$
$\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)$
$\left(\frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}\right)^{2}$
A solid conducting sphere having a charge $Q$ is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be $V$. If the shell is now given a charge of $-3Q$, the new potential difference between the same two surfaces is......$V$
Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:
Two large vertical and parallel metal plates having a separation of $1 \ cm$ are connected to a $DC$ voltage source of potential difference $X$. A proton is released at rest midway between the two plates. It is found to move at $45^{\circ}$ to the vertical $JUST$ after release. Then $X$ is nearly
A table tennis ball which has been covered with conducting paint is suspended by a silk thread so that it hang between two plates, out of which one is earthed and other is connected to a high voltage generator. This ball
Two equal positive point charges are kept at points $A$ and $B$ . The electric potential, while moving from $A$ to $B$ along straight line