Two charges $-q$ and $+q$ are located at points $(0,0,-a)$ and $(0,0, a)$ respectively.

$(a)$ What is the electrostatic potential at the points $(0,0, z)$ and $(x, y, 0) ?$

$(b)$ Obtain the dependence of potential on the distance $r$ of a point from the origin when $r / a\,>\,>\,1$

$(c)$ How much work is done in moving a small test charge from the point $(5,0,0)$ to $(-7,0,0)$ along the $x$ -axis? Does the answer change if the path of the test charge between the same points is not along the $x$ -axis?

In the electric field of a point charge $q$, a certain charge is carried from point $A$ to $B$, $C$, $D$ and $E$. Then the work done

Two equal charges $q$ are placed at a distance of $2a$ and a third charge $ – 2q$ is placed at the midpoint. The potential energy of the system is

The ratio of momenta of an electron and an $\alpha$-particle which are accelerated from rest by a potential difference of $100\, volts$ is

Positive and negative point charges of equal magnitude are kept at $\left(0,0, \frac{a}{2}\right)$ and $\left(0,0, \frac{-a}{2}\right)$, respectively. The work done by the electric field when another positive point charge is moved from $(-a, 0,0)$ to $(0, a, 0)$ is