Two charges of $4\,\mu C$ each are placed at the corners $A$ and $B $ of an equilateral triangle of side length $0.2\, m $ in air. The electric potential at $C$ is $\left[ {\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {{10}^9}\,\frac{{N{\rm{ - }}{m^2}}}{{{C^2}}}} \right]$

If the potential of the inner shell is $10\,V$ and that of the outer shell is $5\,V$, then potential at the centre will be....$V$

Six point charges are kept at the vertices of a regular hexagon of side $L$ and centre $O$, as shown in the figure. Given that $K=\frac{1}{4 \pi \varepsilon_0} \frac{q}{L^2}$, which of the following statement $(s)$ is (are) correct?

$(A)$ the elecric field at $O$ is $6 K$ along $O D$

$(B)$ The potential at $O$ is zero

$(C)$ The potential at all points on the line $PR$ is same

$(D)$ The potential at all points on the line $ST$ is same.

Derive an expression for electric potential at a point due to a system of $\mathrm{N}$ charges.

A hollow metallic sphere of radius $R$ is given a charge $Q$. Then the potential at the centre is

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