First slide

Force on a charged particle moving in a magnetic field

Question

Two charged particles 1 and 2 with same velocity, enter a region of uniform magnetic field in a direction perpendicular to the field. If the particles have the same mass, then

Moderate

A

1 is positively charged and 2 is negatively charged.
B

magnitude of charge of 1 is less than the magnitude of charge of 2
C

magnitude of charges of both particles are the same.
D

1 is negatively charged and 2 is positively charged.

Solution

Force on charged particle moving in magnetic field is given by
$\vec{F} = Q \vec{V} \times \vec{B}$ . This force is the centripetal force. Therefore 1 must carry negative charge and 2 must carry positive charge.
Also trajectories of the particles are circular with radius of curvature $γ = \frac{V_{m}}{Q B_{i}}$ . Since $r_{1} < r_{2} |Q_{1}| > |Q_{2}|$ .

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