Final answer:
In an electromagnetic wave propagating in vacuum, the energy densities stored in the electric and magnetic fields are equal. Thus, half of the wave's total average energy density is stored in the electric field, and half in the magnetic field.
Step-by-step explanation:
In a plane electromagnetic (EM) wave propagating in vacuum, the energies stored in the electric and magnetic fields are equal. The total average energy density u of an EM wave is the sum of the energy density from the electric field UE and the energy density from the magnetic field UB.
As per the suggestion to utilize the time-averaged Poynting vector Sav, which is given by Sav = 1/2 Re {E × H*}, the relationship between electric and magnetic field strengths in vacuum, where c is the speed of light, is given by E = cB. This leads us to understand that the energy densities of the electric and magnetic fields are equal due to the equality ε0 (electric constant) E2 = μ0 (magnetic permeability) B2, indicating that each field contributes equally to the energy density of the wave.
This fact can be mathematically represented as u = UE + UB = ε0 E2 + ½ B2/μ0, which simplifies to u = ε0 E2 (since E = cB and c = 1/√(ε0μ0)). From this expression, it's clear that exactly half of the energy of an electromagnetic wave in vacuum is stored in the electric field, while the other half is stored in the magnetic field.