# What's the reason behind asymmetry of magnetic field in light propagation?

I found in my textbook that

Oscillation of light wave mainly represents the periodic change of electric field $$\vec E$$ as contribution of $$\vec E$$ is the most significant here which creates optical sensation to our eyes.. The direction of the electric vector can be in any direction among all directions on a plane perpendicular to the direction of wave propagation named as electromagnetic wave. But at any given point in time, there will be only one resultant magnetic field.

But according to the figure, I see two fields symmetric here. And 'Ampere's Law' roughly states that 'a changing electric field creates a magnetic field'. Then how can in a particular moment, magnetic field be in any one arbitrary direction?

• Change in electric field creates magnetic field, and vice verse. There is some asymmetry due to absence of magnetic currents and charges, but it does not matter in free space. In media it does matter a bit more.
– Cryo
Jan 7, 2021 at 8:49

In SI units, the E-field amplitude is $$c=3\times 10^8$$ m/s larger than the B-field amplitude. But this is just a consequence of choice of units. It is perfectly possible to adopt a system of units where $$c=1$$ and $$E=B$$. Then, the diagram of the fields at a snapshot in time would be as shown in your question, with similar numbers along the axes perpendicular to the wave propagation direction.
The electric component of the force is $$q\vec{E}$$ and would usually be much larger than the magnetic component $$q\vec{v}\times \vec{B}$$ (in either set of units) unless the charge velocity $$v$$ is an appreciable fraction of the speed of light.
Why this asymmetry? Well, that is how the magnetic field $$\vec{B}$$ is defined. Both $$\vec{E}$$ and $$\vec{B}$$ are not relativistically invariant and are different aspects of one "electromagnetic field".