Question

Show that the time period is independent of both the speed of the iron and radius of the circular path in cyclotron what is the significance of this property

Answer 1

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

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

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

Rearrange the expression for speed v.

v=\frac{qBr}{m}

The time period of ions can be calculated as;

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

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

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

Therefore, the above expression shows that the time period is independent of both the speed of the ion and radius of the circular path in cyclotron.

The significance of this property is that the frequency of revolution of ion remains equal to the frequency of ac source applied.