Question

A cyclotron has frequency f and energy E. If the energy is doubled, frequency becomes

• A. f
• B. 2f
• C. $\frac{f}{2}$
• D. 4f

Hint:

This energy-independence is precisely the principle that allows cyclotrons to work effectively with an alternating voltage of a constant fixed frequency!

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
A cyclotron is a device used to accelerate charged particles outwards from the center along a spiral path.
A fundamental characteristic of a standard non-relativistic cyclotron is that the time period of revolution and the orbital frequency do not depend on the speed or kinetic energy of the particle.
Step 2: Key Formula or Approach:
The orbital cyclotron frequency $f$ of a charged particle of mass $m$ and charge $q$ moving in a uniform magnetic field $B$ is given by the formula:
\[ f = \frac{qB}{2\pi m} \] Step 3: Detailed Explanation:
Looking closely at the formula for the cyclotron frequency $f$, we can observe that it is determined solely by the charge $q$, the magnetic field strength $B$, and the rest mass $m$.
The formula entirely lacks any variable related to the particle's velocity $v$, orbital radius $r$, or kinetic energy $E$.
Therefore, even if the particle accelerates and its kinetic energy is doubled, the frequency of revolution strictly remains unchanged (assuming the speeds remain safely non-relativistic).
Step 4: Final Answer:
The cyclotron frequency remains $f$.