Electromagnetic waves propagate much differently in conductors than they do in dielectrics or in vacuum. If the resistivity of the conductor is sufficiently low (that is, if it is a sufficiently good conductor), the oscillating electric field of the wave gives rise to an oscillating conduction current that is much larger than the displacement current. In this case, the wave equation for an electric field E(x, t)- (0, Ey(x, t), 0) propagating in the +x direction within a conductor is Et) Ot where μ is the permeability of the conductor and rho ls its resistivity A) Check that where kc = νωμ/2p, is a solution of the above wave equation. B) The exponential term shows that the electric field decreases in amplitude as it prop- agates. Explain why this happens. Hint. The field does work to move charges within the conductor. The current of these moving charges causes heating within conductor. Where does this energy come from? C) Note that the electric-field amplitude decreases by a factor of 1/e in a distance 1/ko and calculate this distance for a radio wave with frequency v- 1 MHz in copper (resistivity 1.72 x 10-8 Ω. m, relative permeability μr 1). Since the distance is so short, electromagnetic waves of this frequency can hardly propagate at all into copper Instead they are reflected at the surface of the metal. This is why radio waves cannot penetrate through copper or other metals