Question

A cyclotron designed to accelerate proton has a magnetic field of magnitude 0.450 T over a region of radius 1.02 m. What are (a) the cyclotron frequency and (b) the maximum speed acquired by the protons?

Answer 1

Concepts and reason

The concept used to solve this problem is motion of a proton in a magnetic field.

Initially, the angular frequency of the proton can be calculated by using the relationship between angular frequency, charge of the particle, magnetic field, and the mass of the particle.

Then, the maximum speed of the proton can be calculated from the relationship between the angular frequency, the radius of the path, and the speed.

Fundamentals

A cyclotron is a particle accelerator that uses alternating current to accelerate atomic and subatomic particles in a circular path in a magnetic field.

The expression for the angular frequency is as follows:

Here, is the angular frequency, is the charge of the proton, is the magnetic field and is the mass of the proton.

The expression for the maximum speed is given below:

$V=ro $

Here, is the maximum speed and is the radius.

(a)

The expression for the angular speed is given below:

Substitute for , for , for .

(b)

The expression for the maximum speed is given below:

$V=ro $

Substitute forand for .

Ans: Part a

The angular frequency of the proton is .

Part b

The maximum velocity is .