Question: In a sourceless medium in which J = 0 and = 0, assume a rectangular coordinate system in which E and H are

In a sourceless medium in which J = 0 and ρ_ν = 0, assume a rectangular coordinate system in which E and H are functions only of z and t. The medium has permittivity ∈ and permeability μ.

(a) If E = E_xa_x and H = H_ya_y, begin with Maxwell’s equations and determine the second-order partial differential equation that E_x must satisfy.

(b) Show that E_x = E₀ cos(ωt − βz) is a solution of that equation for a particular value of β.

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