Do E And B Contribute Equally To Light Energy

Question

For light, is energy transport dominated by the electric field, the magnetic field, or both equally?

Short Answer

For a vacuum electromagnetic wave, the correct answer is:

  • both fields contribute equally

Why

The electromagnetic energy density is

[ u = \frac{1}{2}\varepsilon_0 E^2 + \frac{1}{2\mu_0} B^2 ]

The first term is the electric-field contribution and the second term is the magnetic-field contribution.

For a plane wave in vacuum,

[ E = cB ]

and

[ c^2 = \frac{1}{\varepsilon_0 \mu_0} ]

Using these together shows that

[ \frac{1}{2}\varepsilon_0 E^2 = \frac{1}{2\mu_0} B^2 ]

So the electric and magnetic parts of the energy density are equal.

Conclusion

Light energy transport in vacuum is not dominated by only E or only B.

The correct interpretation is:

  • the electric field and magnetic field contribute equally

Counterpoints and Gaps

  • this answer is for vacuum electromagnetic waves
  • in material media, the detailed field-energy bookkeeping can be more subtle