The electric potential $V(x, y, z)$ for a planar charge distribution is given by: 

$V\left( {x,y,z} \right) = \left\{ {\begin{array}{*{20}{c}}
{0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,for\,x\, < \, - d}\\
{ - {V_0}{{\left( {1 + \frac{x}{d}} \right)}^2}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,for\, - \,d\, \le x < 0}\\
{ - {V_0}\left( {1 + 2\frac{x}{d}} \right)\,\,\,\,\,\,\,\,\,\,\,for\,0\, \le x < d}\\
{ - 3{V_0}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,for\,x\, > \,d}
\end{array}} \right.$

where $-V_0$ is the potential at the origin and $d$ is a distance. Graph of electric field as a function of position is given as

$125$ identical drops each charged to the same potential of $50\;volts$ are combined to form a single drop. The potential of the new drop will be......$V$

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

In a region, if electric field is defined as $\vec E = \left( {\hat i + 2\hat j + \hat k} \right)\,V/m$ , then the potential difference between two points $A (0, 0, 0)$ and $B (2, 3, 4)$ in that region, is ......$V$

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]

Assertion: Electron move away from a region of higher potential to a region of lower potential.

Reason: An electron has a negative charge.