10.1 Consider a solid-state plasma with the same number of electrons (e) and holes (h). Using the linearized Langevin equation (with a = e, h)
<J±	0	0
0	<?±	0
0	0	
mQ —- = qa{E + uQ x B0) - i/camQua
at
taking me = m^, i^ce = ^ch, assuming a time dependence for both E and ua of the form exp (-iwt), and choosing a Cartesian coordinate system with the z axis pointing along the constant and uniform magnetic field Bq, show that the conductivity dyad is given by
5 = 2
with <7j_ and gq given by (5.3) and (5.5), respectively. Explain, in physical terms, why we have an — 0 in this case.
= K^f^f (5'3)
(uc - iuj)nce
- („c-M2 + fiS/° (5'4)
nee2 nee2(i/c + iuf)
a° ~~ -/-~t _ -—2\ v*'"*
10.3 Consider the equation J = <5 • E, with S as given in (4.23). If we choose a Cartesian coordinate system such that Ex = E±, Ey = 0, Ez = £?n, and Bo = Bqz (refer to Fig. 2), verify that in this coordinate system we have
Jx = &±E±
Jy - &hE±
Jz = <T||£?|,
Interpret physically this result with reference to Fig. 2.
Fig. 2   Relative orientation of the vector fields E(, Ex, and —E x Bq. The conductivities c^, <r±, and oh govern the magnitude of the electric currents flowing along these directions, respectively.