Find the potential $V$ of an electrostatic field $\vec E = a\left( {y\hat i + x\hat j} \right)$, where $a$ is a constant.

Do free electrons travel to region of higher potential or lower potential ?

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $P$, in the region, is found to vary between in the limits $589.0\,V$ to $589.8\, V$. What is the potential at a point on the sphere whose radius vector makes an angle of $60^o$ with the direction of the field ?........$V$

If the electric potential of the inner metal sphere is $10$ $ volt$ $\&$ that of the outer shell is $5$ $volt$, then the potential at the centre will be ......$volt$

Three charges $q, \sqrt 2q, 2q$ are placed at the corners $A, B$ and $C$ respectively of the square $ABCD$ of side $'a'$ then potential at point $'D'$

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