In the deduction of Alfvén waves, it was assumed that the electrical conductivity of the plasma is infinite. a) Repeat the deduction but for finite electrical conductivity and show that waves are damped. b) How far does the wave travel before dissipating?

Class: Electromagnetics Consider a fixed hollow spherical shell with radius R and surface charge +? (sigma). A particle with mass m and charge -Q that is initially at rest falls in from infinity. Assume that a tiny hole has been cut in the shell to let the charge through. Determine the speed of the particle when it reaches the center of the shell. Your answer should be a function of ? (sigma), Q, and m.

In addition to the "distribution law" - which you have just plotted - Wien also determined a "displace- ment law" which describes the color of the peak in the blackbody spectrum according to b Amax = 7 (1) Here b is some constant which we will determine. (a) Set 4 = 0 to find the wavelength Amax that corresponds to the maximum value of u(A), and use your result to determine the value of the constant b defined in equation (1) above. You should find that b = 0.2014hc/kB, or about 2.9 × 10-3 m · K, a value known as Wien's constant.