A charged particle $q$ is shot towards another charged particle $Q$ which is fixed, with a speed $v$. It approaches $Q$ upto a closest distance $r$ and then returns. If $q$ were given a speed $2v$, the closest distances of approach would be

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?

A charged particle of charge $Q $ is held fixed and another charged particle of mass $m$ and charge $q$ (of the same sign) is released from a distance $r.$ The impulse of the force exerted by the external agent on the fixed charge by the time distance between $Q$ and $q$ becomes $2r$ is

Consider a spherical shell of radius $R$ with a total charge $+ Q$ uniformly spread on its surface (centre of the shell lies at the origin $x=0$ ). Two point charges $+q$ and $-q$ are brought, one after the other from far away and placed at $x=-a / 2$ and $x=+a / 2( < R)$, respectively. Magnitude of the work done in this process is 

The work which is required to be done to make an arrangement of four particles each having a charge $+q$ such that the particles lie at the four corners of a square of side $a$ is .......

How much kinetic energy will be gained by an $\alpha - $particle in going from a point at $70\,V$ to another point at $50\,V$