I Induced Electric and Magnetic Fields Creating Each Other

[bgq]

Hi,

We know that a varying magnetic field creates and induced electric field, and a varying electric field creates an induced magnetic field.

If there is a varying electric field (let's say sinusoidal), then this electric field creates an induced magnetic field. And if this produced magnetic field varies, then it produces an induced electric field. This produced electric field again (if varies) produced another magnetic field and so on. So eventually, we will have an infinite number of electric and magnetic fields. How can we calculate the resultant electric field and the resultant magnetic field? Do Maxwell's equations give the resultant fields, or should we add them by some way?

Thank you.

 

[Ibix]

If there is a varying electric field (let's say sinusoidal), then this electric field creates an induced magnetic field.

Yes. We usually call this light, or electromagnetic radiation generally.

Your "infinite number of electric and magnetic fields" isn't right, though. There's only one EM field, which you can interpret as an electric and a magnetic field. If you care to look at it that way, the electric field is induced by the magnetic field and vice versa. There are no extra fields created anywhere.

 

[bgq]

Yes. We usually call this light, or electromagnetic radiation generally.

Your "infinite number of electric and magnetic fields" isn't right, though. There's only one EM field, which you can interpret as an electric and a magnetic field. If you care to look at it that way, the electric field is induced by the magnetic field and vice versa. There are no extra fields created anywhere.

Thank you

 

[vanhees71]

This is a very common misconception. As can be seen from formulating Maxwell's equations in its natural way as a relativistic field theory one sees that there is one electromagnetic field which can be described by electric and magnetic field components, but this is dependent on the (inertial) frame of reference you perform this split. Only all components together build a physically interpretible observable, the electromagnetic field.

Maxwell's equations also show that you cannot easily interpret the relation between electric and magnetic components in a fixed inertial reference frame as "causing each other". The correct interpretation of, e.g., Faraday's Law
$$\vec{\nabla} \times \vec{E}=-\frac{1}{c} \partial_t \vec{B}$$
is that an electromagnetic field with time-dependent magnetic components implies that there must be electric components forming a vortex, but it does NOT say that the time dependence of the magnetic field causes an electric vortex field or vice versa.

It's of course possible to try to solve for (the solenoidal part of) $\vec{E}$ in terms of $\partial_t \vec{B}$, but finally this leads to complicated non-local relations, which are not of much use for a physical interpretation.

What is causing an electromagnetic field are rather the charge and current distributions. That's clear from looking at "Jefimenko's equations", which express the electromagnetic field as retarded (causal!) integrals over the charge and current distributions (and their derivatives).