On rotating a point charge having a charge $q$ around a charge $Q$ in a circle of radius $r$. The work done will be
$q \times 2\pi r$
$\frac{{q \times 2\pi Q}}{r}$
Zero
$\frac{Q}{{2{\varepsilon _0}r}}$
Work done in moving a positive charge on an equipotential surface is
$(a)$ In a quark model of elementary particles, a neutron is made of one up quarks [ charge $\frac{2}{3}e$ ] and two down quarks [ charges $ - \frac{1}{3}e$ ]. Assume that they have a triangle configuration with side length of the order of ${10^{ - 15}}$ $m$. Calculate electrostatic potential energy of neutron and compare it with its mass $939$ $Me\,V$. $(b)$ Repeat above exercise for a proton which is made of two up and one down quark.
In the figure the charge $Q$ is at the centre of the circle. Work done is maximum when another charge is taken from point $P$ to
The diagram shows a small bead of mass $m$ carrying charge $q$. The bead can freely move on the smooth fixed ring placed on a smooth horizontal plane. In the same plane a charge $+Q$ has also been fixed as shown. The potential atthe point $P$ due to $+Q$ is $V$. The velocity with which the bead should projected from the point $P$ so that it can complete a circle should be greater than
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 .......