Question

A long cylindrical wire carries a positive charge of linear density $\lambda$. An electron $(-e,m)$ revolves aroound it in a circular path under the influence of the attractive electrostatic force. Find the speed of the electron.

Answer 1

Electric field at perprndicular distance $r$
$E=\frac{\lambda }{2\pi {\in }_{0}r}$
the electric force on electron
$F=eE$
To move in circular path, necessary centripital force is provided by electric force.
$F_c=\frac{m{v}^2}{r}=eE=\frac{e\lambda }{2\pi {\in }_{0}r}$
$v=\sqrt{\frac{e\lambda }{2\pi {\in }_{0}m}},v\propto r^0$