Two charged spheres of radii $10\, cm$ and $15\, cm$ are connected by a thin wire. No current will flow, if they have

A sphere of $4\, cm$ radius is suspended within a hollow sphere of $6\, cm$ radius. The inner sphere is charged to potential $3\, e.s.u.$ and the outer sphere is earthed. The charge on the inner sphere is.....$e.s.u.$

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

Ten electrons are equally spaced and fixed around a circle of radius $R$. Relative to $V = 0$ at infinity, the electrostatic potential $V$ and the electric field $E$ at the centre $C$ are

Six charges are placed around a regular hexagon of side length a as shown in the figure. Five of them have charge $q$, and the remaining one has charge $x$. The perpendicular from each charge to the nearest hexagon side passes through the center $O$ of the hexagon and is bisected by the side.

Which of the following statement($s$) is(are) correct in SI units?

$(A)$ When $x=q$, the magnitude of the electric field at $O$ is zero.

$(B)$ When $x=-q$, the magnitude of the electric field at $O$ is $\frac{q}{6 \pi \epsilon_0 a^2}$.

$(C)$ When $x=2 q$, the potential at $O$ is $\frac{7 q}{4 \sqrt{3} \pi \epsilon_0 a}$.

$(D)$ When $x=-3 q$, the potential at $O$ is $\frac{3 q}{4 \sqrt{3} \pi \epsilon_0 a}$.

Uniform electric field of magnitude $100$ $V/m$ in space is directed along the line $y = 3 + x$. Find the potential difference between point $A$ $ (3, 1)$ $\&$ $B$ $(1, 3)$.......$V$