First slide

Magnetic Dipole moment

Question

Two particles, each of mass m and charge q, are attached to the two ends of a light rigid rod of length 2R. The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is

Moderate

A

q/2m
B

q/m
C

2q/m
D

q/ $π$ m

Solution

$\begin{array}{l} M = \frac{2 q}{T} A = \frac{2 q ω}{2 π} π {(R)}^{2} = q ω R^{2} \\ L = 2 m R^{2} (ω) \\ \frac{M}{L} = \frac{q}{2 m} \end{array}$

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