Let's say you have an EM wave propagating along the Z axis.  

If the electric (E) and magnetic (B) fields are described by these two equations:

E = Eo * cos(kz-wt) * ihat   (ihat is the unit vector in the X direction)

B = Bo * cos(kz-wt) * jhat   (jhat is the unit vector in the Y direction)

Is there any detectable or measurable E field outside of the X-Z plane?

Is there any detectable or measurable B field outside of the Y-Z plane?

Do the E,B fields exist at all locations in the X-Y plane or only in their respective planes?



I'm asking this because I am confused by the artwork in my textbook.  The way this is usually drawn in textbooks shows two orthogonal sinusoidal waves (E,B) propagating along the z axis but the sinusoid is drawn entirely in-plane, with no component represented outside the plane.


If I look at derivatives, I get dE/dy = 0.  This could mean E(y>0) = 0 or it could also mean E(y) = invariant with y (constant for all values of y), so no help there.  The same situation exists for b, dB/dx = 0.

Here's a sketch of the situation:



Do Ei and Ej exist (out of plane) or is E restricted to being in the X-Z plane?

For that matter, does E2 exist?



I guess I am just dumb as a rock.  

Polarization can be constant or varying.

If you take a coil pickup and rotate it near a current carrying conductor you will notice it only couples at certain angels.
When the B-field of the current passes through the loop it picks up.
When it is parallel to the loop no pickup.

It is harder to show with the E-field since you need an infinitely sharp probe tip of essentially zero dimension (or a perfect insulator)..

Keep in mind that all models are wrong some models are useful.

These E,B fields are associated with photons traveling on and along the Z axis (center of the circle).  The circle is the profile of a cylindrical surface.

Particle-wave duality.
Photons are not always treated as points.
They have wavelengths and dimensions associated with the fields.

After class, I spoke with the instructor.  He confirmed that the E and B fields exist away from the central axis and that they remain parallel to those fields which are in-plane.  

I asked if the fields are like "a wall" rather than a line and he agreed with that interpretation.  He also said the artwork in the textbook was misleading (shows the field as a line, not a wall).

I have so many more questions about this but am not sure where to ask.  I have a copies of "Physics" by Halliday & Resnick; a copy of Classical Electrodynamics" by Jackson and a Wiley & Sons publication called "Fundamentals of Physics" with no author attribution but it looks a lot like Halliday & Resnick.

I pointed out that the E and B fields both go to zero at the same time (extinguish) and then come back from zero.  I asked where they went and how did they come back from nothing.  

He immediately invoked the wave-particle duality.  

It was fun.

Still, if a photon never has mass and its E-B field energies are extinguished, how does it ever come back from nothingness???


I think there is a lot about this universe we do not understand.  We have descriptions of how things work,... how they behave,... we know the "how" but I think there is no deep understanding of the "why".

Side lobes...

A photon has no rest mass.

It however does have momentum when it is moving.

The coolest thing is that the empirical Maxwell equations are invariant under relativity.

For other weird things the EM waves travel outside of the conductor.

This could be fun.  This field (pun intended) seems to be a great mix of theory/concept, some great math and decent experimentation.

Lots of fun stuff!

Electromagnetic Fields was THE EE wash out course a long time ago.

Probably still is.

The math was a tough nut and before finite element analysis MANY problems had no direct solutions.

Problems with a high level of symmetry at least could be solved.

Seemingly simple problems like printed circuit board trace impedance required a lot of simplifying assumptions to be tractable at all.
FEA has allowed for solutions as exact as you care to spend computer time solving.