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

A small conducting sphere of radius $r$ is lying concentrically inside a bigger hollow conducting sphere of radius $R.$ The bigger and smaller spheres are charged with $Q$ and $q (Q > q)$ and are insulated from each other. The potential difference between the spheres will be

Two tiny spheres carrying charges $1.5 \;\mu\, C$ and $2.5\; \mu\, C$ are located $30 \;cm$ apart. Find the potential and electric field

$(a)$ at the mid-point of the line joining the two charges, and

$(b)$ at a point $10\; cm$ from this midpoint in a plane normal to the line and passing through the mid-point.

At distance of $5$ $cm$ and $10$ $cm $ outwards from the surface of a uniformly charged solid sphere, the potentials are $100$ $V$ and $75$ $V$ respectively . Then

Value of potential at a point due to a point charge is

Two non-conducting spheres of radii $R_1$ and $R_2$ and carrying uniform volume charge densities $+\rho$ and $-\rho$, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region: $Image$

$(A)$ the electrostatic field is zero

$(B)$ the electrostatic potential is constant

$(C)$ the electrostatic field is constant in magnitude

$(D)$ the electrostatic field has same direction