Question

A proton and $\alpha$ particle enter the magnetic field with equal velocities. Which one of these particle experiences more force

• A. proton
• B. $\alpha$ particle
• C. both experiences equal force
• D. can not be predicted

Answer 1

Answer: (B)

$\alpha$ particle

Answer 2

The force experienced by a charged particle moving in a magnetic field is given by the Lorentz force formula:

$\vec{F} = q (\vec{v} \times \vec{B})$

The magnitude of this force is:

$F = q v B \sin\theta$

where:

• $q$ is the magnitude of the charge of the particle.
• $v$ is the magnitude of the velocity of the particle.
• $B$ is the magnitude of the magnetic field.
• $\theta$ is the angle between the velocity vector ($\vec{v}$) and the magnetic field vector ($\vec{B}$).

Given equal velocities, same magnetic field, and assuming the same entry angle, the force is directly proportional to the charge ($q$). A proton has charge $+e$, while an alpha particle has charge $+2e$. Since the alpha particle has twice the charge of a proton, it experiences twice the magnetic force.