Question

If the frequency of the cyclotron is doubled, then the radius becomes?

• A. Doubled
• B. Halved
• C. Quadrupled
• D. Unchanged

Hint:

In a cyclotron, increasing the frequency directly increases the radius of the particle's path. This relationship is key to understanding cyclotron dynamics.

Answer 1

The Correct Option is A

In a cyclotron, the radius of the particle's path is given by the formula: \[ r = \frac{mv}{qB} \] where: - \( m \) is the mass of the particle, - \( v \) is the velocity of the particle, - \( q \) is the charge of the particle, - \( B \) is the magnetic field strength. For a cyclotron, the velocity \( v \) is related to the frequency \( f \) by: \[ v = 2\pi rf \] where \( r \) is the radius and \( f \) is the frequency. If the frequency is doubled, the radius will also double to maintain the relationship, because the velocity is proportional to the frequency. Thus, when the frequency of the cyclotron is doubled, the radius becomes doubled.