Question

show that time period of ions in a cyclotron is independent of both the speed and radius of circular path..!

Answer 1

Explanation:

The centripetal force is needed by the ions in a cyclotron to move in a circular track is provided by the force due to the magnetic field.

$\frac{mv^2}{r}=qvB$

Here, m is the mass of the charged particle, v is the speed of the charged particle, q is the charge, B is the magnetic field and r is the radius.

Rearrange the expression for speed v.

$v=\frac{qBr}{m}$

Calculate the time period of ions.

$T=\frac{2\pi r}{v}$

Put $v=\frac{qBr}{m}$.

$T=\frac{2\pi m}{qB}$

Therefore, the time period of ions in a cyclotron is independent of both the speed and radius of circular path.