Homework Help: Magnetic moment of a particle suspended in a magnetic field?

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1. Oct 15, 2014

Derive the following expressions for ux, uy and uz:
ux(t) = ux(0) cos(wo t) + uy(0) sin(wo t)
uy(t) = - ux(0) sin(wo t) + uy(0) cos(wo t)
uz(t) = uz(0)
wo is angular frequency.
wo = g Bo

2. Relevant equations
wo of this precession is proportional to Bo
u and J have the same orientation:
u = g J, where g is gyromagnetic ratio.
du/dt = u X g B (where X is cross product)

3. The attempt at a solution
u
= ux i + uy j + uz k
B
= B k
u
X B = (ux i + uy j + uz k) X (B k) = -ux B j + uy B i
u
X g B = -ux g B j + uy g B i = uy g B i - ux g B j
du/dt = u X g B
du/dt = uy g B i - ux g B j
Therefore,
dux/dt = uy g B
duy/dt = -ux g B
duz/dt = 0

I do not know how to proceed. From duz/dt = 0, we get uz = constant = uz(0)
But how to derive the expressions for ux and uy?

2. Oct 20, 2014