How can we deduce the kink effect in the electric field?

[AhmedHesham]

Hi.

In videos online the kink is explained as a delay in the electric field when charges accelerate. Does this mean we can deduce the existence of kinks from coloumb law. Does the simple form of plane electromagnetic waves which is well treated in most books really exist.

What is the relationship between accelerating charges and plane electromagnetic waves. How can we deduce the kink effect from Maxwell equations . What's really an electromagnetic waves . Is it a propagating kink or a cascade of electric and magnetic fields creating each other

I know it's both. But how. It's not properly explained.

Thanks

 

[vanhees71]

I've no clue, which "kink" you are referring to.

For sure plane waves are idealizing limits but not exactly realizable in nature since they would imply an infinite electromagnetic field energy. Plane waves are good local approximations for really existing waves very far from all sources (i.e., time-dependent charge-current distributions).

Coulomb's law is not sufficient to derive the existence and properties of electromagnetic waves. For that you need to full set of time-dependent Maxwell equations. The predictions of electromagnetic waves and their properties was the greatest achievement by Maxwell, making his model much better than any other then existing model about electromagnetism. Particularly it also united the two large topics of electromagnetism and optics into one theory. It's one of the milestones on the physicists's way to a comprehensive unified theory of all of nature, which has not been fully achieved yet though.

 

[Nugatory]

How can we deduce the kink effect from Maxwell equations?

By a “kink” you mean the way the electric field changes in pictures like this (and similar diagrams found in many textbooks and all over the internet)?

Those are usually drawn assuming that charge changes place instantaneously, and of course that’s not really possible. However, you can analyze the problem rigorously using Maxwell’s equations and assuming that the charge moves quickly but not instantaneously (that is, no infinite speed or acceleration). If the motion is abrupt enough you’ll get a picture that looks like the kink picture propagating outwards. However, the calculations are rather messy; I don’t think I’ve ever seen it done except with a computer and numerical techniques.

The closest experimental realization is probably a spark-gap transmitter; that’s fairly easy to duplicate with the right equipment.

 

[Nugatory]

What's really an electromagnetic waves . Is it a propagating kink or a cascade of electric and magnetic fields creating each other

Both. That “cascade” you describe is the plane-wave solution of Maxwell’s equations. Maxwell’s equations are linear, which means that if $A$ and $B$ are solutions, so is $A+B$ - we can build up complex waveforms by adding together (“superimposing”) simpler solutions. It turns out that just about any waveform, including that outwards-propagating kink, can be written as a superposition of plane waves.

 

[vanhees71]

No I understand what's meant in the OP. Of course the kink is just the kink you introduced by the sudden change of the velocity of the particle, i.e., you use something like $\vec{v}=\vec{v}_0 \Theta(t)$. That's of course an artificial situation which is only used for illustrative purposes, because it can be evaluated analytically using the Lienard-Wiechert retarded solutions of Maxwell's equations.

 

[tech99]

Apologies for offering a qualitative description, which I do with trepidation.
If you imagine the charges in a wire, they can be made to accelerate sinusoidally by passing an alternating current through it. When you do this, a wave of compression and rarefaction passes at nearly the speed of light along the charges in the wire. Charges move slowly, but each charge carries out a small sinusoidal excursion. For a wire, the accelerating charges are electrons, because the residual atom, or positive ion, is too heavy to move quickly. At some distance from the wire, we see a field from every electron and an opposite field from every positive ion. By superposition, we see zero static field, but that is not to say the fields are not there. Suppose we have a picture of electric field lines, admittedly a 19th Century concept. Visualise one field line from an electron, and you will see a sinusoidal kink traveling away from the electron. This constitutes a transverse electric field, and there is no opposing transverse field from the heavy positive ion. You can make a model of this process by taking a slinky and tying a dangling thread of wool to it part way along. The thread represents a field line and the slinky represents a wire. When you send a compression wave along the slinky, a transverse wave is created on the woollen thread, the field line.
When the transverse electric field passes an observer, they see an accompanying in-phase magnetic field, as per Maxwell.