Question

Two electrons \( e_1 \) and \( e_2 \), both having mass \( m \) and charge \( q \), are projected perpendicular to a magnetic field \( B \). If the kinetic energy of \( e_1 \) is twice that of \( e_2 \), what is the relation between their rotation frequencies \( f_1 \) and \( f_2 \)?

• A. \( f_1 = f_2 \)
• B. \( f_1 = 2f_2 \)
• C. \( 2f_1 = f_2 \)
• D. \( 4f_1 = f_2 \)

Hint:

Cyclotron frequency depends only on charge, magnetic field, and mass: \( f = \frac{qB}{2\pi m} \)

Answer 1

The Correct Option is A

Cyclotron frequency is independent of speed or kinetic energy: \[ f = \frac{qB}{2\pi m} \] Since both electrons have the same charge and mass, the frequency of rotation is the same, regardless of kinetic energy difference.