# Energy of an electromagnetic wave

## Main Question or Discussion Point

I'm trying to teach myself some basic physics, and so maybe this question is stupid! But according to the wave model, the energy in an EM wave is proportional to the energy in the E and B fields, which can assume a range of values, no? But according to the quantum model, the energy of a photon is simply proportional to the frequency of the light. There seems to be a contradiction here. What am I missing?

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Drakkith
Staff Emeritus
The basic answer is that Quantum Mechanics is ultimately correct. An EM wave is made up of many photons, each of which has a discrete, quantized energy value, so the energy of an EM wave is the sum of the energy of every photon.

Jano L.
Gold Member
But according to the wave model, the energy in an EM wave is proportional to the energy in the E and B fields, which can assume a range of values, no? But according to the quantum model, the energy of a photon is simply proportional to the frequency of the light. There seems to be a contradiction here. What am I missing?
Could you please state more carefully where do you see the contradiction? The two sentences talk about different things; the wave and the photon.

jtbell
Mentor
For a system with a very large number of photons (any macroscopically measurable electromagnetic field), you can relate the average number of photons per unit volume to the strength of the classical electric and magnetic fields via the energy per unit volume.

BruceW
Homework Helper
although, there doesn't need to be any energy per unit volume. There could just be a plane wave which is transporting energy, which has zero energy per volume.

But yeah, I think that is the rough idea. The energy of a classical EM wave is given by both the frequency of the wave and the amplitude of the electric and magnetic fields. So, we can relate the frequency of the wave to the frequency of each of the photons, and the amplitude of the fields to the number of photons per volume.

edit: wait, no sorry, that's totally incorrect. there does need to be energy per unit volume, which is proportional to E2+B2