As per the diagram a point charge +q is placed at the origin O. Another point charge -Q  is displaced from the point A [coordinates (0, a)] to another point B [coordinates (a, 0)] along the straight path AB .Total work done  is this process will be --

       

A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is :

You are to bring two charges ${\mathrm{q}}_{1 }\mathrm{and} {\mathrm{q}}_2$from infinity to the point represented by the potential ${\mathrm{V}}_1\mathrm{and} {\mathrm{V}}_2$ in an electrical field $\mathrm{E}.$. If the distance between ${\mathrm{q}}_1 \mathrm{and} {\mathrm{q}}_2$ within the field is $r$. Find the total work done in assembling the configuration.

 Imagine an electric field  $\mathrm{E}=\left(20\widehat{ \mathrm{i}}+30\widehat{ \mathrm{j}}\right) {\mathrm{NC}}^{-1}$ in a space. The potential at the origin is zero Find the potential at the $\left(2,2\right)\mathrm{m}$,

A point particle of mass $0.5 \mathrm{kg}$ is moving along the $X$ -axis under a force described by the potential energy $V$ shown below. It is projected towards the right from the origin with a speed $v$.

What is the minimum value of $v$ for which the particle will escape infinitely far away from the origin?

Four point charge (with equal magnitude of charge of $5 C;$ but with different signs) are placed at four corners of a square of side $10 \mathrm{m}.$ Assuming that the square is centered at the origin and the configuration of the charges are as given in the figure, the potential and the magnitude of electric field at the origin, respectively are

[Note $\left.k=\frac{1}{4\pi {\epsilon }_0}\right]$

Van de Graaff generator consists of a hollow metal sphere of diameter $2 \mathrm{m}$. If the potential on the surface of the sphere is $6$ million volt, the charge accumulated over the surface of the sphere is: