A thin circular disk of radius R is uniformly charged with density σ 0 per unit area. The disk rotates about its axis with a uniform angular speed ω. The magnetic moment of the disk is :

Question

A thin circular disk of radius R is uniformly charged with density σ > 0 per unit area. The disk rotates about its axis with a uniform angular speed ω. The magnetic moment of the disk is : (A) π R4σω (B) (π R4/2)σω (C) (π R4/4)σω (D) 2π R4σω

Tardigrade Admin · Accepted Answer

(q/2M) = (Magnetic dipole moment/Angular momentum) ∴ Magnetic dipole moment (M) M = (q/2M). ((MR2/2))ω = (1/4)σ.π R4ω

Q. A thin circular disk of radius $R$ is uniformly charged with density $σ$ > 0 per unit area. The disk rotates about its axis with a uniform angular speed $ω$ . The magnetic moment of the disk is :

$π R^{4} σω$

$\frac{π R ^{4}}{2} σω$

$\frac{π R ^{4}}{4} σω$

$2 π R^{4} σω$

$\frac{q}{2 M} = \frac{M a g n e t i c d i p o l e m o m e n t}{A n gu l a r m o m e n t u m}$
$∴$ Magnetic dipole moment (M)
$M = \frac{q}{2 M} . (\frac{M R ^{2}}{2}) ω$
$= \frac{1}{4} σ . π R^{4} ω$

Q. A thin circular disk of radius R is uniformly charged with density σ > 0 per unit area. The disk rotates about its axis with a uniform angular speed ω. The magnetic moment of the disk is :

πR4σω

2πR4​σω

4πR4​σω

2πR4σω