Question

Two electrons (each of charge = e and mass = m) are attached one at each end 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 angular momentum about the axis of rotation to the magnetic dipole moment of the system is

Answer 1

Answer on Question #68047 - Physics / Electromagnetism

Question:

Two electrons (each of charge = e and mass = m) are attached one at each end 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 angular momentum about the axis of rotation to the magnetic dipole moment of the system is

Solution:

Angular momentum:

$$L = I \omega , I = 2 m r ^ {2}, L = 2 m r ^ {2} \omega$$

Magnetic moment:

$$B = \frac {\mu \mu_ {0} A}{2 r}, A = \frac {q}{t} = \frac {\omega q}{2 \pi} = \frac {\omega e}{\pi}, B = \frac {\mu \mu_ {0} \omega e}{2 \pi r}$$

The ratio:

$$\frac {L}{B} = \frac {4 m \pi r ^ {3}}{\mu \mu_ {0} e}$$