Write an equation for potential due to volume charge distribution.

The electric potential inside a conducting sphere

For given $\vec E = 2x\hat i + 3y\hat j$, find the potential at $(X, Y)$ if potential at origin is $5\, volts.$

Some charge is being given to a conductor. Then its potential 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 $\frac{3 q}{4 \sqrt{3} \pi \epsilon_0 a}$.

Two metal spheres of radii ${R_1}$ and ${R_2}$ are charged to the same potential. The ratio of charges on the spheres is