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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.

enter image description here

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?

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    $\begingroup$ 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. $\endgroup$
    – Cryo
    Jan 7, 2021 at 8:49

2 Answers 2

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You may be reading the text in an unintended way. You can replace electric and magnetic and the sentence is stil true. The condition is for them to be reciprocally perpendicular but you can rotate the two fields together around an axis along the direction of propagation. This is, for an unpolarized beam. You could say that the magnetic field can have an arbitray direction and the electric field is perpendicular to the magnetic field. You can think about an L-shaped, representing the two fields. The size of the legs oscillate in time and space. The only condition is that the plane of the figure is perpendicular to the propagation direction (in vacuum and many media). There is nothing special about one of the legs, in term of direction. Of course,

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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.

Where there is an asymmetry is with the effect that the fields have on charges.

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".

In terms of direction of the fields there is no asymmetry there. The E- and B-fields are both in the plane perpendicular to the wave propagation direction and mutually perpendicular. We may choose to define the direction of one field and then that completely determines the direction of the other.

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