Two particles, \'A\' with charge and mass of q and m and \'B\' with charge and m

Question

Two particles, 'A' with charge and mass of q and m and 'B' with charge and mass of -q and 2m, each enter at right angles to a uniform magnetic field with the same velocity. Compare the circular paths that each begin upon entering the magnetic field.

A) A experiences the same force magnitude as that of B and circulates in the same direction as B with A's radius equal to that of B.
B) B experiences twice force magnitude as that of A and circulates in the opposite direction as A with A's radius at half that of B.
C) B experiences twice force magnitude as that of A and circulates in the opposite direction as A with A's radius equal to that of B.
D) A experiences the same force magnitude as that of B and circulates in the opposite direction as B with A's radius at half that of B.

Explanation / Answer

answer is (D) the force on B is the same as that on A because magnetic force F = qvB when the velocity is at right angles to the field, in other words F is directly proportional to q. Since the charges are identical in magnitude, so are the forces. The direction is opposite because the force is in the opposite direction because the charges are of opposite sign. Finally, the radius for B is twice that for A because the formula for Larmor radius r = mv/qB shows that radius is directly proportional to mass.

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