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Dynamic magneto conductivity tensor for free electrons a metal with a concentration n of free electrons of charge – e is in a static magnetic field B. The electric current density in the xy plane is...

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Dynamic magneto conductivity tensor for free electrons a metal with a concentration n of free electrons of charge – e is in a static magnetic field B. The electric current density in the xy plane is related to the electric field by jx = sxxEx + sxyEy; jy = syzET + syyEy. Assume that the frequency w >> w0, and where w >> 1/t, where wc = eB/mc and t is the collision time.
(a) Solve the drift velocity equation (51) to find the components of the magneto conductivity tensor:
sxx = syy + iw2p/4pw;sxy = – syx = wcw2p/4pw2, where w2p = 4pne2/m.
(b) Note from a Maxwell equation that the (dielectric function tensor of the medium is related to the conductivity tensor as e = 1 + i(4p/w)s. Consider an electromagnetic wave with wave vector k = kz. Show that the dispersions relation for this wave in the medium is c2k2 = w2 – w2p ± wc w2p/w
At a given frequency there are two modes of propagation with different wave vectors and different velocities. The two modes correspond to circularly polarized waves. Because a linearly polarized wave can he decomposed into two circularly polarized waves, it follows that the plane of polarization of a linearly polarized wave will he rotated by the magnetic field.
Answered Same Day Dec 24, 2021

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David answered on Dec 24 2021
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