Question

An electron (of charge $-e$) revolves around a long wire with uniform charge density $\lambda$ in a circular path of radius $r$. Its kinetic energy is given by:

• A. $\frac{\lambda e}{8\pi {ϵ}_{0}r}$
• B. $\frac{\lambda e}{4\pi {ϵ}_{0}r}$
• C. $\frac{\lambda e}{2\pi {ϵ}_{0}r}$
• D. $\frac{\lambda e}{4\pi {ϵ}_0}$

Answer 1

The correct option is D $\frac{\lambda e}{4\pi {ϵ}_0}$

Electric field for infinitely long wire is given by $E=\frac{\lambda }{2\pi {\epsilon }_{0}r}where\lambda =ch\arg edensity$

Since the electron is revolving then the centripetal force is balanced by the electrostatic force

$F_e=F_c$

$eE=\frac{m{v}^2}{r}$

$\frac{e\lambda }{2\pi {\epsilon }_0}=m{v}^2$

$\frac{e\lambda }{4\pi {\epsilon }_0}=\frac{1}{2}m{v}^2$

$KE=\frac{e\lambda }{4\pi {\epsilon }_0}$