E & B field phase relationship in EMR

[ChrisXenon]

TL;DR Summary

Shouldn't they be 90 degrees out of phase?

Common diagrams for the magnetic and electric field components of EMR show the fields at right angles in space with peaks aligned along the axis of propogation, for example Wikipedia here: https://en.wikipedia.org/wiki/Electromagnetic_radiation.

However, Faraday's law says the E field depends on the rate of change of the B field. At it's maximum the B field's reate of change is zero, and so the E field should be zero. So the peaks should not coincide. The E field peak should be wheredB/dt is max - which is when B is passing through zero. So the fields should be 90 degrees out of phase.

No?

 

[sophiecentaur]

Summary: Shouldn't they be 90 degrees out of phase?

No?

No. The solutions to Maxwell's Equations produce a free space wave with E and H in phase.
Right next to a radiating structure, the fields (near field) will be in quadrature but there is a gradual transition from one situation to the other as distance increases over the first few wavelengths (or more).

It bothered me, too, at one time when comparing EM waves with mechanical waves, in which the interchange between Kinetic and Potential energy produces peaks of displacement and velocity which are, indeed, in quadrature - so the flow of energy is constant. Not the case with EM.

 

[ChrisXenon]

sophiecentaur - thanks. What a luxury to have easy and near-instant access to such knowledgeable people.
If I could prevail upon your good nature again - is there an easy explanation of why this gradual transition takes place? Or even thename of a phenomenum without the explanation? What is it that puishes this gradual transiation?

 

[Dale]

Faraday's law says the E field depends on the rate of change of the B field. At it's maximum the B field's reate of change is zero, and so the E field should be zero.

This is slightly wrong in a very important way. Faraday’s law actually says $\nabla \times E=-\partial B/\partial t$. So it is not the E field itself that depends on the rate of change of the B field, but the curl of the E field which is a spatial derivative. So Faraday’s law says that the spatial rate of change in the E field is proportional to the temporal rate of change of the B field.

For a sinusoidal plane wave the zero crossing is both the greatest temporal change and the greatest spatial change. So the E and B fields must be in phase.

 

[sophiecentaur]

is there an easy explanation of why this gradual transition takes place?

The fields reduce at different rates. The Radiating Field falls off at 1/r. The near fields are 'reactive'; the E field falls off as 1/r² and the H field falls off as 1/r³. Have look at this link as a starter.

 

[sophiecentaur]

Not only are the local fields not what you'd expect but the actual directions they point can be a bit surprising. Looking at the top end of a simple dipole. the E field near its axis is pointing the opposite way to the radiated field (as with the field lines around a bar magnet which point 'up' at the pole and 'down' at points out towards the sides). The situation with a plane wave out in space is a lot easier to visualise.

 

[ChrisXenon]

Thanks for your replies guys. I found I'm not knowledgeable enough to understand them so I'll need to do some learning but I appreciate your time & effort.

 

[tech99]

The fields reduce at different rates. The Radiating Field falls off at 1/r. The near fields are 'reactive'; the E field falls off as 1/r² and the H field falls off as 1/r³. Have look at this link as a starter.

Not sure the reactive H field always falls with 1/r^3. If you are close to the wire, the field tends to initially fall off as 1/r. This is confusing, because the radiated magnetic field does the same.