Question

An infinitely long positively charged wire has a linear charge density 'lamda' C/m.An electron is revolving around the wire as its centre with a constant velocity in a circular plane perpendicular to the wire.Deduce the expression for its kinetic energy.

Answer 1

Dear Student

Electric field due to straight wire
$$\begin{gathered} E=\frac{\lambda }{2\pi r} \\ ForceonelectronduetothiselectricfieldF=eE \\ Thisforcewillprovidecentripetalforce \\ eE=\frac{m{v}^2}{r} \\ m{v}^2=reE \\ \frac{1}{2}m{v}^2=\frac{1}{2}reE \\ K.E.=\frac{1}{2}re\left(\frac{\lambda }{2\pi r}\right) \\ K.E.=\frac{\lambda e}{4\pi } \end{gathered}$$

Regards