Question

Two charged particles enter a uniform magnetic field normally. If the ratio of the specific charges of the two particles is 2:3, then the ratio of the times taken by the two particles to complete one revolution is:

• A. 1:1
• B. 3:2
• C. 9:4
• D. 3:2

Hint:

Period in uniform magnetic field depends on mass-to-charge ratio: $T = 2\pi m/(qB)$.
Specific charge $q/m$ is key to compare periods.
Inverse proportionality: higher q/m → smaller period.

Answer 1

The Correct Option is B

• Cyclotron motion period $T = \dfrac{2\pi m}{qB} = \dfrac{2\pi}{B} \cdot \dfrac{1}{q/m}$.
• Given $q_1/m_1 : q_2/m_2 = 2:3$.
• Period ratio $T_1 : T_2 = (m_1/q_1) : (m_2/q_2) = (1/(q_1/m_1)) : (1/(q_2/m_2)) = 3:2$.
• Hence correct answer: 3:2.