Question

A point charged particle is revolving around a long straight charged wire under influence of electrostatic force. If radius of circular path is r, then the time period (T) is proportional to

Answer 1

Time period (T) is proportional to r

Explanation:

Electric field at a distance $r$ from a infinite straight wire having charge density $\lambda$ C/m is given by

$E=k\frac{2\lambda}{r}$     (where k is Coulomb's constant)

Force at a point charge $q$ at a distance [/tex]r[/tex] from wire

$F=qE$

This force will provide the necessary centripetal acceleration

If angular velocity is $\omega$ and mass is $m$

Then

$mr\omega^2=\frac{2\lambda k}{r}$

$\implies\omega=\sqrt{\frac{2\lambda k}{mr^2}}$

$\implies \omega=\frac{1}{r}\sqrt{\frac{2\lambda k}{m}}$

Time period

$T=\frac{2\pi}{\omega}$

$\implies T=2\pi r\sqrt{\frac{m}{2\lambda k}}$

Thus we can see that

$T\propto r$

Hope this answer is helpful.

Know More:

Q: A charged particle Q is fixed and another charged particle of mass m and charge q of same sign is  released from distance r. The impulse of force exerted by external agent on fixed charge by the time distance between Q and q becomes 2r is:

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