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When looking at a diagram of the electric and magnetic fields oscillating down the time axis of a light ray diagram the field amplitude and frequency of each component is shown equal. Are they in fact equal in both respects?

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In general, if you have a travelling wave at some frequency $f$, then both the electric and magnetic fields will oscillate at that same frequency.

However, the amplitudes of the waves are generally not comparable, and they're only drawn as equal for visual convenience. The reason for this is that the units of electric field and magnetic field don't generally match, so trying to compare an electric field amplitude (of, say, 1 V/m) with a magnetic field amplitude (of, say, 1 T) is completely meaningless.

In certain unit systems this comparison can indeed be made, with the most prominent example being CGS units, where electric and magnetic fields have the same physical dimension and are therefore comparable; in this system the electric and magnetic field amplitudes for a plane wave are exactly equal. In other systems, such as SI units, no such comparison can be made.

On the other hand, even if the amplitudes $E_0$ and $B_0$ cannot be compared, one thing you can do is compare the relative amount of energy stored in the electric and magnetic field oscillations, given by $\frac{\varepsilon_0}2E_0^2$ and $\frac{1}{2\mu_0}B_0^2$, respectively, and here it's easy to see that regardless of the system of units both components, magnetic and electric, carry exactly equal amounts of energy, at least for a plane wave.

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Electromagnetic field in free space is described by linear partial differential equations. You can choose a basis of the solutions that have equal amplitudes and frequencies of the electric and magnetic fields (if you use a certain system of units). However, an arbitrary solution of the equations will be a superposition of the solutions from the basis, so it will have some distributions of frequencies for the electric and magnetic fields, and the amplitudes of the electric and magnetic fields do not have to be equal (and it is not even obvious that they can be reasonably defined).

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