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

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 (A) q/2m (B) q/m (C) 2q/m (D) q/ π m

Tardigrade Admin · Accepted Answer

Current, i = (frequency) (charge) = ( ( ω/2 π )) (2 q) = (q ω /π ) Magnetic moment, M = (i) (A) = ( ( q ω/ π ) ) (π R2 ) = (q ω R2 ) Angular momentum, L = 2 I ω = 2 (m R2) ω ∴ (M/L) = (q ω R2/2 (mR2) ω ) = ( q/2m)

q/2m

q/m

2q/m

$q / πm$

Current, i = (frequency) (charge) = $(\frac{ω}{2 π}) (2 q) = \frac{q ω}{π}$
Magnetic moment, $M = (i) (A) = (\frac{q ω}{π}) (π R^{2}) = (q ω R^{2})$
Angular momentum, $L = 2 I ω = 2 (m R^{2}) ω$
$∴ \frac{M}{L} = \frac{q ω R ^{2}}{2 ( m R ^{2} ) ω} = \frac{q}{2 m}$

q/2m

q/m

2q/m

q/πm

Current, i = (frequency) (charge) = (2πω​)(2q)=πqω​ Magnetic moment, M=(i)(A)=(πqω​)(πR2)=(qωR2) Angular momentum, L=2Iω=2(mR2)ω ∴LM​=2(mR2)ωqωR2​=2mq​

$q / πm$

Current, i = (frequency) (charge) = $(\frac{ω}{2 π}) (2 q) = \frac{q ω}{π}$
Magnetic moment, $M = (i) (A) = (\frac{q ω}{π}) (π R^{2}) = (q ω R^{2})$
Angular momentum, $L = 2 I ω = 2 (m R^{2}) ω$
$∴ \frac{M}{L} = \frac{q ω R ^{2}}{2 ( m R ^{2} ) ω} = \frac{q}{2 m}$