Two charges of magnitude $5\, nC$ and $-2\, nC$ are placed at points $(2\, cm, 0, 0)$ and $(x\, cm, 0, 0)$ respectively in a region of space where there is no other external field. If the electrostatic potential energy of the system is $-0.5\,\mu J$, find the value of $x$ in $cm$.

The electric potential in volts due to an electric dipole of dipole moment $2 \times 10^{-8} \, C \cdot m$ at a distance of $3 \, m$ on a line making an angle of $60^{\circ}$ with the axis of the dipole is ..........

Write an equation of electric potential at a point on the axis of an electric dipole.

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?

Three point charges of $2 \ mC$ each are kept at the vertices of an equilateral triangle of side $50 \ cm$. If the system is supplied energy at the rate of $2 \ kW$,the time taken to move one of the charges to the midpoint of the line joining the other two charges is (in $s$)

Obtain the equation of electric potential energy of a dipole from the equation of potential energy of a system of two electric charges.