Eight charges, each of magnitude $\mathrm{q}$ are placed at the vertices of a cube placed in vacuum. Electric potential at the centre of the cube due to this system of charges is:

( ${\mathrm{\epsilon }}_0$ is permittivity of vacuum and $a$is length of each side of the cube)

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 :

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

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?

The diagrams below show regions of equipotential.



A positive charge is moved from $A$ to $B$ in each diagram.

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: