Question

If \( q \) is electric charge, \( B \) is magnetic field, \( R \) is the dee radius and \( m \) is the mass of ions, the kinetic energy of the ions in cyclotron is given by:

• A. \( \frac{qBR}{2m} \)
• B. \( \frac{qBR}{m} \)
• C. \( \frac{q^2 B^2 R^2}{4m} \)
• D. \( \frac{q^2 B^2 R^2}{2m} \)

Hint:

For cyclotron motion, the kinetic energy is related to the charge, magnetic field, radius, and mass of the ion as \( \frac{q^2 B^2 R^2}{2m} \).

Answer 1

The Correct Option is D

The kinetic energy of ions in a cyclotron is given by the formula \( \frac{q^2 B^2 R^2}{2m} \), derived from the motion of charged particles in a magnetic field. Thus, the correct answer is option (4).