Write an equation for an electrostatic potential of a negative point charge. 

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.

The linear charge density on a dielectric ring of radius $R$ varies with $\theta $ as $\lambda \, = \,{\lambda _0}\,\cos \,\,\theta /2,$ where $\lambda _0$ is constant. Find the potential at the centre $O$ of ring. [in volt]

Assume that an electric field $\overrightarrow E  = 30{x^2}\hat i$ exists in space. Then the potential difference $V_A -V_O$, where $V_O$ is the potential at the origin and $V_A$ the potential at $x = 2\, m$ is

Six point charges are placed at the vertices of a regular hexagon of side $a$ as shown. If $E$ represents electric field and $V$ represents electric potential at $O$, then

A solid conducting sphere, having a charge $Q$, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be $V$. If the shell is now given a charge of $-4\, Q$, the new potential difference between the same two surface is......$V$