Question

A charged particle moves with a velocity $V$ in a circular path of radius $R$ around a long uniformly charged conductor then

• A. $V\propto R$
• B. $V\propto \frac{1}{R}$
• C. $V\propto \frac{1}{\sqrt{R}}$
• D. $V$ is independent of $R$

Answer 1

The correct option is D $V$ is independent of $R$

Electric field at a distance R due to a uniformly charged conductor $E=\frac{\lambda }{2\pi {ϵ}_{o}R}$

Force on the charge particle $F_e=qE=\frac{\lambda q}{2\pi {ϵ}_R}$

Centripetal force on the charge particle $F_c=\frac{m{V}^2}{R}$

Equating $F_c=F_e$

$\frac{\lambda q}{2\pi {ϵ}_{o}R}=\frac{m{V}^2}{R}$

$⟹V^2=\frac{\lambda q}{2\pi {ϵ}_{o}m}$

Thus $V$ is independent of $R$.