An electric charge $10^{-6} \mu \mathrm{C}$ is placed at origin $(0,0)$ $\mathrm{m}$ of $\mathrm{X}-\mathrm{Y}$ co-ordinate system. Two points $\mathrm{P}$ and $\mathrm{Q}$ are situated at $(\sqrt{3}, \sqrt{3}) \mathrm{m}$ and $(\sqrt{6}, 0) \mathrm{m}$ respectively. The potential difference between the points $P$ and $Q$ will be :

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 $\frac{3 q}{4 \sqrt{3} \pi \epsilon_0 a}$.

Two thin wire rings each having a radius $R$ are placed at a distance $d$ apart with their axes coinciding. The charges on the two rings are $ + q$ and $ – q$. The potential difference between the centres of the two rings is

A charge of $10 \,\mu C$ is placed at the origin of $x-y$ coordinate system. The potential difference between two points $(0, a)$ and $(a, 0)$ in volt will be

Two conducting spheres of radii $R_1$ and $R_2$ are charged with charges $Q_1$ and $Q_2$ respectively. On bringing them in contact there is