Dispersion of magnetic permeability LL 8 section 79

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

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

A result of magnetostatics. There were no timedependent electric fields

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 d. P/dt. A weak electric field E would also give a small P, but this cannot be satisfied for electromagnetic waves where E ~ H.

To find the condition on w where d. P/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

Magnetization Magnetic susceptibility To get We need

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 d. P/dt << c curl M

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

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