Question

A cyclotron with a magnetic field of 0.47 t is designed to accelerate protons in a circle with a radius 0.68 m. What is the angular frequency of the proton?

Answer 1

The angular frequency of the cyclotron is 0.07 x $10^{8}$Hz.

What is angular frequency?

• Angular frequency, abbreviated "ω" is a scalar measure of rotation rate in physics.
• It describes the rate of change of the argument of the sine function, the rate of change of the phase of a sinusoidal waveform, or the angular displacement per unit of time.

What is cyclotron?

The cyclotron device is made to accelerate charge particles to extremely high speeds by applying crossed electric and magnetic fields.

Calculation of angular frequency:

Given,

B = 0.47 T

r = 0.68

mass of proton = 1.6x$10^{-27}$

q = 1.6 x $10^{-19}$

so, the frequency is:

f = qB/2$\pi$m

f = 1.6 x $10^{-19}$ x 0.47/2x3.14x1.6x$10^{-27}$

f = 0.07 x $10^{8}$

Hence, the angular frequency of the cyclotron is  0.07 x $10^{8}$Hz.

Learn more about angular frequency here:

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