Question

A charged particle moves with a speed v in a circular path of radius r around a long uniformly charged conductor.The conductor has charge per unit length $\lambda$. The particle has mass m and charge q , then :

• A. $v\propto \sqrt{q}$
• B. $v\propto \sqrt{\lambda }$
• C. $v\propto \sqrt{m}$
• D. $v\propto \frac{1}{\sqrt{m}}$

Answer 1

Answer: (A), (B), (D)

$v\propto \sqrt{q}$
$v\propto \sqrt{\lambda }$
$v\propto \frac{1}{\sqrt{m}}$

The electric field at a distance r from the long charged conductor is $E=\frac{1}{4\pi {ϵ}_0}.\frac{2\lambda }{r}$

For equilibrium, the centrifugal force balance the electrostatic force between the charged particle and the long charged conductor. i.e,

$\frac{m{v}^2}{r}=qE=\frac{q}{4\pi {ϵ}_0}.\frac{2\lambda }{r}$

or $v=\sqrt{\frac{q}{4\pi {ϵ}_0}.\frac{2\lambda }{m}}$

$\therefore v\propto \sqrt{q},v\propto \sqrt{\lambda },$ and $v\propto \frac{1}{\sqrt{m}}$