Question

A cyclotron with a magnetic field of 1.2 T is used to accelerate protons. How does the time for the protons to complete one orbit change when the radius of their orbit changes from 10 cm to 22 cm? Multiple Choice

A. It increases by a factor of 2.2.

B. It decreases by a factor of 2.2.

C. It increases by a factor of 4.8.

D. It decreases by a factor of 4.8.

E. It stays the same.

Answer #1

The force exerted by the magnetic field is balanced by the centripetal force of the particle.

mv²/r = qvB where v is the velocity of the particle and r is the radius of the circular path. So v = qBr/m

The above equation shows that the velocity of the particle varies proportional to the radius of the circular path. From the first relation we can derive the relation for the time period of the cyclotron T = 2/ where is the angular velocity and = v/r. So time period

T = 2m/qB ie, time period doesn't depend on the radius of the path. So the time period of the proton in this case will remain same if we change the radius of the path. So option E is correct.

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