# On Electromagnetic Radiation and how it propagates through space.

Hello everybody.

I've been having difficulty in understanding how an electromagnetic wave propagates through space.

Firstly, from what I understand, electromagnetic waves are made up of a constantly varying electric field placed perpendicular and in phase with a constantly varying magnetic field. Now lets set up a source to generate an electromagnetic wave. From the above, the source should consist of a varying electric field and varying magnetic field.

Now consider a point P a distance d away from the source. The time taken for the energy from the wave to reach the point P from the moment the source is switched on would then be
t = d/c.

Isn't the effect of a magnetic or electric field assumed to be instant before relativity showed that information cannot be transfered faster than the speed of light?

Even so, how does 2 perpendicular fields explain how energy is transfered through space? From what I've read from texts its because the electric field induces a magnetic field (Maxwell's law of induction), and the induced magnetic field induces yet another electric field (Faraday's law of induction) and so and so forth. But I failed to understand that as it still does not seem to explain how the wave propagates through space. The induced B-fields and E-fields are still induced in the space about the source, and I'm unable to see how it travels.

Perhaps someone could point me in the right direction?

Let us consider two still and equal charges put very close to each other. It will be our source. At large distances we observe nothing due to neutralisation (cancelation) the static fields from close charges. Then we make one charge oscillate with some amplitude around another charge. The dipole moment d=e*r(t) varies in time and this creates the filed perturbations (differences) noticable at long distances. As soon as the field equations predict retardation of the perturbation arrival to some distant point, we will see the field changes starting from t=D/c, not before. If the frequency is very low, we will see a quasi-instantenious propagation. (Static fields do not propagate, they are always present and determined with the actual charge positions.)

Now, the electric and magnetic fields are coupled not only in time (due to time derivatives ∂/∂t) but also in space due to space derivatives ∇. This makes waves in space: the field amplitudes at different space points are different.

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Let us assume the oscillating charged particle makes one full oscillation. This causes the electric field and magnetic field to go through one cycle of variation. How does this energy move from the source to the point P? Shouldn't the effects of the magnetic and electric field be felt immediately without any relativistic considerations?

No, there is no instant propagation. There is always a retardation time D/c. For slowly moving charges (small charge displacements during D/c, r(t) ≈ r(t-D/c)) it looks as instantenious but it is not in reality. The small dimentionless parameter is v/c:

r(t) ≈ r(t-D/c) => r(t) - r(t-D/c) ≈ r(t) - r(t) + (dr/dt)*D/c ~ v/c.

Let us consider an atim in an excited state. At far distances we see nothing - the system is neutral and does not create any wave. Then atom undergoes a transition to its ground state and emits a photon (due to change, for example, atomic dipole or quadrupole moment). We will see the photon arrival at t= D/c, not before.

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So in other words, the wave propagates through space due to the electric and magnetic forces being 'felt' only after a time t = d/c?

I mean, I've read that information cannot travel faster than the speed of light, but I've had the impression that it wasn't around during the Maxwell days but yet they were able to understand EM waves effectively.

Thanks for the help anyway.

... but I've had the impression that it wasn't around during the Maxwell days but yet they were able to understand EM waves effectively.

Maxwell pretty quickly realized that his equations (about the 1860's) spelled out a speed for electromagnetic waves of that of light..in other words they were the same thing. He kind of unified "light" (visible) with the rest of the electromagnetic spectrum.....

What was not realized for sometime was that light/electromagnetic waves actually propagate in a vacuum..."ether" was the favorite theory for a while..until the Michaelson-Morely experiment failed to detect ether...about 20 years later....so the "absolute" speed of light (c in all inertial frames) was implied but not fully understood for a while...in 1905 Einstein clinched that...

I've been having difficulty in understanding how an electromagnetic wave propagates through space.

Me too.....it's pretty crazy (for me anyway) to think that such energy produced billions of years ago, just after the big bang, is still propagating around the universe...the cosmic background radiation......you'd think it would have disappeared by now....

Hello everybody.

I've been having difficulty in understanding how an electromagnetic wave propagates through space.

Isn't the effect of a magnetic or electric field assumed to be instant before relativity showed that information cannot be transfered faster than the speed of light?

Even so, how does 2 perpendicular fields explain how energy is transferred through space? From what I've read from texts its because the electric field induces a magnetic field (Maxwell's law of induction), and the induced magnetic field induces yet another electric field (Faraday's law of induction) and so and so forth. But I failed to understand that as it still does not seem to explain how the wave propagates through space. The induced B-fields and E-fields are still induced in the space about the source, and I'm unable to see how it travels.

Note that since information cannot travel faster than the speed of light that sets the limit on the propagation of electric and magnetic fields. That effect is called "retardation". ALL effects are propagated at the speed of light or less. The alternative theory is called "action at a distance" and has been long discredited and abandoned except by those working in Quantum Mechanics.

Please note that a electric field DOES NOT induce a magnetic field and a magnetic field DOES NOT induce an electric field. Those statements though widespread are incorrect. Thus the commonplace "explanation" using Maxwell's equations of how a wave propagates by E and B "creating" each other is totally bogus. The mistake is often compounded by assuming that E and B are 90 degrees out of phase. They are NOT. They are in phase! The mistake arises by the (false) assumption that EM waves propagate by a mechanism analogous to how energy bounces back and forth in an oscillating LC circuit. However, in that case the explanation IS correct. For EM waves, the source is an accelerated charge (current) which thus creates a wave that propagates in some manner though empty space.

So one has to ask how does ANY wave "propagate"? In mechanics it has to do with stress and strain. If one stresses a certain part of the medium, that stress is passed on to the next element of the medium and that next element stresses the next element and so on. IF there are few losses it turns out the disturbances more or less follow what are called solutions to the wave equation that are sinusoidal. One would assume that the same sort of mechanism holds in the electromagnetic case.

Only things aren't so simple. The original theory was that the EM stresses were in a medium known as "the aether" that filled space. Today physicists mostly believe the dogma that EM waves are propagated in "nothing at all". In other words without the stress transmission needed for other physical waves to propagate. And wait! It gets still worse. We are only talking about classical descriptions. Today it is widely assumed that EM waves are not classical waves at all but just similar versions of the light particles known as "photons" so easily observed in the IR/visible/UV ranges. In such a case one would then assume that radio waves aren't waves at all but some kind of particles with wave-like properties. Well, we know how particles propagate. They just zip through space! But how do their wave-like properties propagate in nothing at all? Who knows? It's a mystery.

Dale
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Even so, how does 2 perpendicular fields explain how energy is transfered through space? From what I've read from texts its because the electric field induces a magnetic field (Maxwell's law of induction), and the induced magnetic field induces yet another electric field (Faraday's law of induction) and so and so forth. But I failed to understand that as it still does not seem to explain how the wave propagates through space. The induced B-fields and E-fields are still induced in the space about the source, and I'm unable to see how it travels.
Note that what Faraday's law really says is that if an electric field is changing in space in a particular way then the magnetic field is changing in time. Similarly Ampere's law says that (in the absence of any sources) if a magnetic field is changing in space in that same way then the electric field is changing in time. The spatial part is already inherently in Maxwell's equations.

Awesome. Thanks guys. Because most of the equations I read started with the assumption that it was a wave and then moved on to prove its speed and so forth, but never really explicitly showed that it was a wave before hand, by description or otherwise.

Another small question though. When was the 'action at a distance' found to be incorrect? If I'm not wrong, during Newton's days everyone believed that the effects of any change in gravitation would be 'felt' immediately by all observers all the way up to its maximum range, which is, in theory, infinity. Was action at a distance discredited during, before or after the days of Maxwell's equations? If not during those days, everyone would still have believed in action at a distance, while at the same time understanding waves in the classical sense.

I seem to have gotten the impression that the limit was only realized after Einstein showed relativistic theory proved that there was indeed an upper limit placed on the speed of transfer of information. Am I mistaken?

Born2bwire