Time Period of Charged Particles in Magnetic Field – Rankers Physics

Force Acting on Moving Charges: Practice Problem & Solution

Assertion (A): If a proton and an \( \alpha \)-particle enter a uniform magnetic field perpendicularly, with the same speed, then the time period of revolution of the \( \alpha \)-particle is double than that of proton. Reason (R): In a magnetic field, the time period of revolution of a charged particle is directly proportional to mass.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Force Acting on Moving Charges. Understanding the underlying formula is key to arriving at the correct answer below:

The time period is \( T = \frac{2\pi m}{qB} \). For a proton, \( T_p = \frac{2\pi m_p}{eB} \). For an \( \alpha \)-particle, \( T_\alpha = \frac{2\pi (4m_p)}{2eB} = 2 \frac{2\pi m_p}{eB} = 2T_p \). So, A is true. Reason R (\( T \propto m \)) is true, but it's not the complete explanation for A, as \( T \) also depends on \( q \).

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