The potential at a distance $R/2$ from the centre of a conducting sphere of radius $ R$ will be

A hollow metallic sphere of radius $10 \;cm$ is charged such that potential of its surface is $80\; V$. The potential at the centre of the sphere would be

The potential at a point, due to a positive charge of $100\,\mu C$ at a distance of $9\,m$, is

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

An electric field $\vec E\, = (25 \hat i + 30 \hat j)\,NC^{-1}$ exists in a region of space. If the potential at the origin is taken to be zero then the potential at $x\, = 2\, m, y\, = 2\, m$ is......$volt$

If eight identical drops are joined to form a bigger drop, the potential on bigger as compared to that on smaller drop will be