A sinusoidal electromagnetic wave has an electric field whose rms value is 100 V/m.What is the instantaneous rate S of energy flow for this wave? A)1.7 * 10^-4 W/m² B)13 W/m² C)27 W/m² D)1.0 * 10⁵ W/m² E)4.0 * 10¹⁰ W/m²

Question

Quizplus · Accepted Answer

The instantaneous rate of energy flow (Poynting vector) for a sinusoidal electromagnetic wave is given by S = (1/μ₀) E₀B₀, where E₀ and B₀ are the peak values of the electric and magnetic fields, respectively, and μ₀ is the vacuum permeability. For a sinusoidal wave, the rms value of the electric field is equal to E₀/√2. Therefore, we can find E₀ = 100√2 V/m. The peak value of the magnetic field is given by B₀ = E₀/c, where c is the speed of light. Thus, B₀ = (100√2)/(3×10⁸) T. Using μ₀ = 4π×10⁻⁷ T·m/A, we can calculate S as S = (1/μ₀) E₀B₀ = 27 W/m². Therefore, the answer is C.

A Sinusoidal Electromagnetic Wave Has an Electric Field Whose Rms