Charge $q_{2}$ is at the centre of a circular path with radius $r$. Work done in carrying charge $q_{1}$, once around this equipotential path, would be
$\frac{1}{4 \pi \varepsilon_{0}} \times \frac{q_{1} q_{2}}{r^{2}}$
zero
$\frac{1}{4 \pi \varepsilon_{0}} \times \frac{q_{1} q_{2}}{r}$
infinity
Electrostatic potential energy of given system will be
If $4 \times {10^{20}}eV$ energy is required to move a charge of $0.25$ coulomb between two points. Then what will be the potential difference between them......$V$
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
This question contains Statement$-1$ and Statement$-2$. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement$-1$ : For a charged particle moving from point $P$ to point $Q$, the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q$.
Statement$-2$ : The net work done by a conservative force on an object moving along a closed loop is zero.
Calculate potential energy of a point charge $-q$ placed along the axis due to a charge $+ Q$ uniformly distributed along a ring of radius $R$. Sketch $P.E.$ as a function of axial distance $z$ from the centre of the ring. Looking at graph, can you see what would happen if $-q$ is displaced slightly from the centre of the ring (along the axis) ?