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