Angular speed in terms magnetic field

[sept26bc]

Homework Statement

3. A particle with magnetic dipole moment of magnitude μ (be careful—this is not a magnetic
permeability) and spin angular momentum of magnitude S is immersed in a magnetic field
of magnitude B. For simplicity, assume that the spin and magnetic-moment vectors (which
are either in the same or opposite directions) are perpendicular to the magnetic field. The
particle will precess, i.e., its spin angular momentum vector will rotate about the direction
of the magnetic field, with angular speed Ωp.
Find Ωp, in terms of the properties of the particle and the magnetic field. HINT: Remember
that Newton’s Second Law for rotation states that the torque equals the rate of change of
angular momentum.

Homework Equations

I did have to substitute in the variable notation given in the problem for the following equations.
Im not entirely sure what equations to use. But I've jotted down these.
angular momentum (S)= moment of inertia (I) x angular speed (Ωp)
precession angular velocity= T/L= ωr/Iω
Magnetic Field: B= mΩp/q

b]3. The Attempt at a Solution [/b]

B = mΩp/q
= m (S/I)/ q

I solve B for Ωp and Ωp= Bq/m

μ= q/2m S S is the angular momentum
solve μ for q then but that in Ωp equation

so I then got:

Ωp= B2μ/S

Does this make any sense?

 

[anathema]

Hello there! Your solution looks good so far. Just a couple of things to note:

1. In the equation B = mΩp/q, B represents the magnitude of the magnetic field, not the magnetic moment. So you should use B = mΩp/q = mS/I instead of B = mΩp/q = mμ/S.

2. The magnetic moment here is not the same as the magnetic permeability. The magnetic moment (μ) is a measure of the strength of the particle's magnetic field, while the magnetic permeability (μ0) is a measure of how easily a material can be magnetized. So you should not substitute μ for q in your equation for Ωp.

With those corrections, your final answer should be Ωp = Bμ/S. Great job!