Question

In Cyclotron, the frequency of revolution ofthe charged particle in a magnetic field is independent of

• A. its mass
• B. its energy
• C. oscillatory frequency
• D. magneric fiel
• E. its charge

Answer 1

The Correct Option is B

Cyclotron Frequency Independence 

In a cyclotron, we want to determine what the frequency of revolution of a charged particle in a magnetic field is independent of.

Step 1: Cyclotron Frequency Formula

The cyclotron frequency (\(f\)) is the frequency at which a charged particle revolves in a uniform magnetic field. It's given by:

\(f = \frac{qB}{2\pi m}\)

Where:

• \(f\) is the cyclotron frequency.
• \(q\) is the magnitude of the charge of the particle.
• \(B\) is the magnitude of the magnetic field.
• \(m\) is the mass of the particle.

Step 2: Dependence on Energy

From the formula, we can see that the frequency \(f\) depends on the charge \(q\), the magnetic field \(B\), and the mass \(m\). It does *not* directly depend on the energy of the particle. However, this is true only for non-relativistic speeds. At relativistic speeds, the mass of the particle increases with its energy, and thus the frequency does become energy-dependent. *For the standard introductory physics treatment of the cyclotron, however, we assume non-relativistic speeds*.

Conclusion

Assuming non-relativistic speeds, the frequency of revolution of the charged particle in a magnetic field in a cyclotron is independent of its energy.

Answer 2

In a cyclotron, the frequency \( f \) of a charged particle is given by the formula: \[ f = \frac{qB}{2\pi m} \] where:
\( q \) is the charge of the particle
\( B \) is the magnetic field strength
\( m \) is the mass of the particle

From this equation, we can see that the frequency depends on the charge \( q \), magnetic field \( B \), and mass \( m \), but it does not depend on the energy of the particle. This is because the energy influences the velocity of the particle, but the frequency of revolution remains unaffected by the speed (and hence the energy) of the particle. Thus, the frequency of revolution is independent of its energy.