(a) A homogeneous medium is characterized by a magnetic susceptibility m . Use Faradays law to...

(a) A homogeneous medium is characterized by a magnetic susceptibility χ_m. Use Faraday’s law to show that the magnetization current J = ∇ × M can be expressed in the form

This result can be regarded as a special case of a homogeneous medium that obeys Ohm’s law with a conductivity tensor that is non-diagonal, non-local in time, and non-local in space. That is, the total current can be written in the form

(b) Expand E(r', t') in a Taylor series around E(r, t) and show that j_i (r, t) contains a piece consistent with the form of J_i (r, t). Comment on the other pieces you find. What happens if the system is invariant to the symmetry operation of inversion (r→ −r)?

Transcribed Image Text:

Ji (r, t) = Xm xa) Jar fanaka - dt' Sij мо(1 + Xm) 22 2x;дх }E E;(r, t').