The ratio of average electric energy density and total average energy density of electromagnetic wave is :

Solution

Physics sir · 3 steps

In an EM wave the electric and magnetic fields carry equal energy, so the electric part is exactly half.

1. Two energy densities. The average electric energy density is u_E = 1/4ε₀ E₀² and the average magnetic energy density is u_B = 1/4B₀²/μ₀. The factor 1/4 comes from averaging sin² over a cycle, which gives 1/2.
2. They are equal. Use B₀ = E₀/c and c² = 1/(μ₀ ε₀). Then B₀²/μ₀ = E₀²/(μ₀ c²) = ε₀ E₀², so u_B = u_E.

   u_E/(u_E + u_B) = u_E/2u_E = 1/2

3. So. The electric part is half of the total average energy density. The ratio is 1/2, option (d).

The idea to keep. In any EM wave in free space, energy is shared equally between the electric and magnetic fields. Each field carries half the total, at every instant and on average.

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