6.1.1. In terms of the standard units mass kg, length m, time s, and charge C, show that ( ? ₀ ? ₀) ^-1/2 has the units of a velocity.

6.1.2. Prove that E( z, t) and H( z, t) are orthogonal in a vacuum for an arbitrary function of ( z - ct).

6.2.1. Let F( z - ct) = 1 and G( z + ct) = -2 for z - ct ? 1 and z + ct ? 1, respectively, and F( z - ct) = G( z + ct) = 0 elsewhere. Accurately sketch the pulse with the velocity c = 2 at three times: t = 0, t = 1, and t = 3.

Note: Normalized variables are used.

6.2.2. Define the functions F( z - v ₁ t) and G( z + v ₂ t) from the following sketch, which was drawn at the times t = 0 and t = 2.

6.2.3. If the waves in Problem 2 were electromagnetic waves, find the ratio of the dielectric constants ? ₂ and ? ₁ for the two regions ( z < 0)/( z > 0) if the relative permeabilities were...