For the plane electromagnetic wave given by E=E₀ sin (ω t-k x) and B=B₀ sin (ω t-k x), the ratio of average electric energy density to average magnetic energy density is

Solution

Physics sir · 3 steps

Use E₀ = cB₀ and c² = 1/μ₀ε₀: the two energy densities come out exactly equal.

1. Average energy densities. The average of sin² over a cycle is 1/2. So the average electric energy density is 1/4ε₀ E₀² and the average magnetic energy density is 1/4μ₀ B₀².
2. Link the amplitudes. In an EM wave the amplitudes are tied by E₀ = cB₀, and the speed of light is c = 1/√(μ₀ ε₀).

   u_E/u_B = (1/4ε₀ E₀²)/(1/4μ₀B₀²) = μ₀ε₀ E₀²/B₀² = μ₀ε₀ c² = 1

3. So. The ratio is 1: the wave carries its energy equally in the electric and magnetic fields, so the answer is (a).

The idea to keep. In any EM wave in vacuum, the electric and magnetic fields carry equal energy, both at every instant and on average. The total energy density is just twice either one.

Answer from the NTA final answer key. Solution by PrepWiser.