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
$\frac{{{q^2}}}{{8\pi {\varepsilon _0}a}}$
$\frac{{6{q^2}}}{{8\pi {\varepsilon _0}a}}$
$ - \frac{{7{q^2}}}{{8\pi {\varepsilon _0}a}}$
$\frac{{9{q^2}}}{{8\pi {\varepsilon _0}a}}$
A proton of mass $m$ and charge $e$ is projected from a very large distance towards an $\alpha$-particle with velocity $v$. Initially $\alpha$-particle is at rest, but it is free to move. If gravity is neglected, then the minimum separation along the straight line of their motion will be
Three identical small electric dipoles are arranged parallel to each other at equal separation a as shown in the figure. Their total interaction energy is $U$. Now one of the end dipole is gradually reversed, how much work is done by the electric forces.
For an infinite line of charge having charge density $\lambda $ lying along $x-$ axis, the work required in moving charge $q$ from $C$ to $A$ along arc $CA$ is :-
Obtain equation of electric energy of a single charge.
A positively charged ring is in $y-z$ plane with its centre at origin. A positive test charge $q_0$, held at origin is released along $x$-axis, then its speed