First slide

Force on a charged particle moving in a magnetic field

Question

An electron and a proton are injected into a uniform magnetic field perpendicular to it with the same momentum. What is the nature of their trjaectories?

Easy

A

Both move along circular path and radius of curvature is less for electron.
B

Both move along circular path and radius of curvature is less for proton
C

Radius of curvature is same for both
D

Both move along straight lines.

Solution

Linear momentum $p = m V \Rightarrow V = \frac{p}{m}$ and angular frequency $ω = Q B / m$ . Both of the particles will move along circular path. Radius of curvature, $γ = \frac{V}{ω} = \frac{p}{m} \times \frac{m}{Q B} = \frac{p}{Q B}$ charge Q is same for both. So option (3) is right.

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