Assertion and Reason: Charged Particles in Magnetic Field – Rankers Physics

Force Acting on Moving Charges: Practice Problem & Solution

Assertion (A): An electron and a proton enter a uniform magnetic field at right angles to the field with equal velocities, then, deviation of both from the original path will be the same. Reason (R): In the situation described above, electron and proton will experience magnetic forces of different magnitude.  
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 magnitude of magnetic force \( F = qvB sin\theta \) will be the same for an electron and a proton as their charge magnitudes \( q \), velocities \( v \), and magnetic field \( B \) are identical, and \( \theta = 90^\circ \). So (R) is false. The radius of the circular path is \( r = mv/(qB) \). Since \( m_e \ll m_p \), then \( r_e \ll r_p \). Therefore, the electron will deviate more than the proton. So (A) is false. Both (A) and (R) are false.

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