Question

Two particles of the same mass have charges in the ratio 3 : 1. What is the ratio of their time periods when they enter a constant magnetic field with the same velocity?

• A. \( 3 : 1 \)
• B. \( 1 : 3 \)
• C. \( 9 : 1 \)
• D. \( 1 : 9 \)

Hint:

The time period of a charged particle in a magnetic field is inversely proportional to the charge. So, the higher the charge, the shorter the time period.

Answer 1

The Correct Option is B

The time period \( T \) of a charged particle moving in a magnetic field is given by: \[ T = \frac{2\pi m}{qB} \] where \( m \) is the mass of the particle, \( q \) is the charge, and \( B \) is the magnetic field strength. Since the particles have the same mass and enter the same magnetic field with the same velocity, the time period depends on the charge. The ratio of the time periods is given by the ratio of the charges: \[ \frac{T_1}{T_2} = \frac{q_2}{q_1} \] Given that the charges are in the ratio 3 : 1, the time period ratio will be: \[ \frac{T_1}{T_2} = \frac{1}{3} \]
Thus, the ratio of the time periods is \( 1 : 3 \). Hence, the correct answer is \( 1 : 3 \).