Two particles, each of mass m and charge q , are attached to the two ends of a light, rigid rod of length 2 R . The rod is rotated at a 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

Question

Two particles, each of mass m and charge q , are attached to the two ends of a light, rigid rod of length 2 R . The rod is rotated at a 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, q 2 m, q m, 2 q m, q π m

MARKS App · Accepted Answer

Current, i = (frequency) (charge) = ω 2 π 2 q = q ω π Magnetic moment, M = i A = q ω π π R 2 = q ω R 2 Angular momentum, L = 2 I ω = 2 mR 2 ω ∴ M L = q ω R 2 2 mR 2 ω = q 2 m

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