For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric (Uₑ) and magnetic (Uₘ) fields is :

Solution

Physics sir · 4 steps

Use E = cB and you will see the electric and magnetic fields carry exactly equal shares of the energy.

1. Write both densities. The electric field stores uₑ = 1/2ε₀ E² per unit volume. The magnetic field stores uₘ = B²/2μ₀ per unit volume.
2. Link E and B. In free space the two fields of the wave are tied together by E = cB, with c = 1/√(μ₀ ε₀). So B² = E²/c² = μ₀ ε₀ E².

   uₘ = B²/2μ₀ = (μ₀ ε₀ E²)/2μ₀ = 1/2ε₀ E² = uₑ

3. Take the average. This equality holds at every instant and at every point, so it holds for the averages too. Each average equals 1/4ε₀ E₀², where E₀ is the peak field.
4. So. Uₑ = Uₘ, which is option (a). Each field carries half of the total energy density.

The idea to keep. In an EM wave in free space, energy is split equally between the electric and magnetic fields. E = cB is the bridge that turns one energy density into the other.

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