Ampere’s circuital law states that the line integral of the magnetic field B around any closed circuit is equal to the permeability constant times the current I passing through the circuit.

Magnetic field due to straight infinite current carrying wire

For a long straight line, magnetic field around a circular loop will be constant and tangent at every point.

Also,

∴

As B is constant

⇒

∴

Difference between magnetic and electrostatic field lines is:

Magnetic field lines form closed loops whereas electrostatic field lines do not. Magnetic field lines are produced by the moving charges whereas electrostatic field lines are produced by static charges.

OR

Principle of a cyclotron:

A charged particle can be accelerated to the very high energies by passing it through electric field many times using the fact that frequency of revolution is independent of energy of a charged particle.

Let a particle of charge q and mass m enters a region of magnetic field B with velocity v normal to the field. It follows a circular path where centripetal force is provided by the magnetic field.

⇒

So,

The time period of revolution will be,

Hence, time period of revolution of particles in a cyclotron is independent of their speeds.

This property necessary for the operation of a cyclotron so that the frequency of revolution of particle remains equal to the frequency of ac source applied to the cyclotron.