Question

A point charge $q$ is revolving in a circle of radius ${}^{\prime }{r}^{\prime }$ around a fixed infinite line charge with positive charge $\lambda$ per unit length. Now the point charge is shifted and it revolves in a circle of radius $2r$. Then :

• A. speed of the point charge $q$ remain constant
• B. speed of the point charge $q$ will be change
• C. angular velocity of the point charge $q$ about line charge does not change
• D. work done by all forces is non-zero

Answer 1

The correct option is A speed of the point charge $q$ remain constant

Electric field at distance $r$ from the infinite line charge is $E=k\frac{2\lambda }{r}$
The necessary centripetal force to the point charge of mass $m$ is provided by electrostatic attraction.
$\therefore \frac{m{v}^2}{r}=qE=qk\frac{2\lambda }{r}$ or $v=\sqrt{\frac{2k\lambda q}{m}}$
The speed of charged particle is independent of orbital radius. Hence the K.E. of point charge in orbits of radius $r$ and $2r$ is same. As the work done is the change of K.E, so the work done by all forces is zero.