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Khan Academy

A transverse electromagnetic wave (TEM) in a coaxial waveguide has an electric field 𝐄=𝐄(ρ, φ) e^i(k z-ωt) and a magnetic induction field of 𝐁=𝐁(ρ, φ) e^i(k z-ωt). Since the wave is transverse, neither 𝐄 nor 𝐁 has a z component. The two fields satisfy the vector Laplacian equation ∇^2 𝐄(ρ, φ) =0 ∇^2 𝐁(ρ, φ) =0 . (a) Show that 𝐄=ρ̂ E0(a / ρ) e^i(k z-ωt) and 𝐁=φ̂ B0(a / ρ) e^i(k z-ωt) are solutions. Here a is the radius of the inner conductor and E0 and B0 are constant amplitu