1. Dispersion of magnetic permeability
LL8 section 79

2. Permittivity e(w) approaches unity at UV frequencies.
Permeability m(w) approaches unity at much lower frequencies (microwaves).
Then magnetic induction B = mH = H
And magnetization (magnetic moment per unit volume) M = (B – H)/4p = 0

3. - The total magnetic moment of a body is
This is the microscopic current density averaged over atomic dimensions
Maxwell equations
Substract
M = (B – H)/4p -

4. A result of magnetostatics
A result of magnetostatics. There were no time-dependent electric fields

5. What conditions allow neglect of
For a given w, a small body dimension l gives large spatial derivatives in
So that this term would dominate over dP/dt.
A weak electric field E would also give a small P, but this cannot be satisfied for electromagnetic waves where E ~ H.

6. To find the condition on w where dP/dt can be neglected and magnetization can be important, place the body on the axis of a solenoid with variable current.
Then the electric field E appears only due to induction
This should be small compared to c curl M

7. Magnetization
Magnetic susceptibility
To get
We need

8. There is another constraint: We are working in the limit where macroscopic electrodynamics is applicable.
Magnetic susceptibility has meaning only in that limit.
The body has to be bigger than one atom for averaging over atomic dimensions to be possible.
l >> a
Combine both conditions:
Macroscopic ED
dP/dt << c curl M

9. Electron velocity
In the optical range, we can estimate magnitudes as
And
Atomic oscillating dipoles are sources of optical photons
Is the condition for neglecting dP/dt compared to c curl M at optical frequencies.
This cannot be satisfied.

10. There is no meaning to using a magnetic susceptibility in the optical range.