# Is a changing B-field identical to a changing E-field in an electromagnetic wave?

1. Feb 8, 2010

### diagopod

I'm learning that in the electrodynamics of circuits and charges, an E-field is very different from a B-field. But in Maxwell's equations for a disturbance in the electromagnetic field, where a changing electric field causes a changing magnetic field, which in turn causes a changing electric field, etc, I can't tell if there's essentially any difference between the two fields in that context, and the diagrams of the transverse e.m. wave indeed make them look identical, just at right angles to each other. Is there any trace of their difference left in this context, or are they essentially the same in the context of an e.m. disturbance?

2. Feb 8, 2010

### Bob S

Re: Is a changing B-field identical to a changing E-field in an electromagnetic wave

The E vector of radiation from an half-wave (electric) dipole antenna is aligned along the length of the antenna (and the accelerating current). The direction of the E field in Rayleigh scattering is aligned along the direction of the electric dipole of the induced dipole oscillation. So yes there is a difference, the polarization of the E and H vectors in EM radiation retain the polarization of their source.

Bob S

3. Feb 8, 2010

### diagopod

Re: Is a changing B-field identical to a changing E-field in an electromagnetic wave

Thanks Bob. So is the only difference the direction of polarization? In other words, is it merely semantics to call one the B-field, and the other the E-field, or is there something beyond their orthogonal orientation toward one another, some property that distinguishes an E-field intrinsically from a B-field? Thanks for bearing with me on this.

4. Feb 8, 2010

### Bob S

Re: Is a changing B-field identical to a changing E-field in an electromagnetic wave

The E-field is intrinsically different than the B-field. The E-field can excite the electric dipole moment in atoms and materials, determines the emission direction of low-energy photoelectrons, determines the reflection/refraction characteristics (including Brewster's angle reflection) of incident light, etc. There are many effects, such as Faraday rotation, Kerr effect, Voight effect, QMR effect, Pockels cells, etc. that are either electro-optic or magneto-optic effects in origin.
Bob S
[added]Low energy scattered light off of free electrons (Thomson scattering) is polarized along the electric vector (scattering is in plane perpendicular to E vector). At higher energies, photon scattering off of free electrons (Klein Nishina (Compton) scattering) also has polarization effects. Magnetically-oriented ferrite suspensions in a magnetic field can polarize light (H-vector I think) along the B field direction..

Last edited: Feb 8, 2010
5. Feb 8, 2010

### diagopod

Re: Is a changing B-field identical to a changing E-field in an electromagnetic wave

Thanks Bob. appreciate you guiding me through this. So yes, I'm becoming acquainted with the genuine difference b/w the E-field and B-field in the context of charges, materials and many other contexts. The gist of my questions is whether, solely in the context of an electromagnetic wave itself, where a changing magnetic field causes a changing electric field, back and forth, there is any difference other than one field being orthogonal to the other. The "transverse wave" diagrams that are so common, such as this one (http://www.molphys.leidenuniv.nl/monos/smo/basics/images/wave_anim.gif [Broken]), seem to say that they are really the same in this one context, but are these diagrams glossing over an important difference in the two fields as they create one another in an e.m. disturbance?

Last edited by a moderator: May 4, 2017
6. Feb 8, 2010

### Bob S

Re: Is a changing B-field identical to a changing E-field in an electromagnetic wave

There is one important distinction between E and H that I did not tell you about earlier. This relates to the Poynting vector, which determines the direction of propagation. Using a right-handed cartesian coordinate system x y z, if the E vector is along x, and the H vector is along y, then the direction of propagation is along z.

Bob S

7. Feb 8, 2010

### Born2bwire

Re: Is a changing B-field identical to a changing E-field in an electromagnetic wave

Many will argue that when it comes to electromagnetic waves, it is all electromagnetism. That is, the moment you have time-varying fields you intrinsically have both electric and magnetic fields. This is a case of being correct, the best kind of correct, technically correct. While most people, myself included, will say that a changing X field will induce a changing Y field (interchange X and Y with B, H, E or D as you please), the physics can be massaged to show that really it's all or nothing. For example, Jefimenko's equations ( http://en.wikipedia.org/wiki/Jefimenko's_equations ) show how a source inherently produces both the electric and magnetic fields thereby eliminating any serious notions of one being causally linked to the other. Instead, they both exist.

That is not to say that they are the same. Their relationships and physical effects are different. As mentioned previously, their polarization dictates the power flow via the Poynting vector. In addition, the resulting forces on charged particles are different as seen in the Lorentz force equation.

8. Feb 9, 2010

### diagopod

Re: Is a changing B-field identical to a changing E-field in an electromagnetic wave

Thanks Bob. I was actually looking at the Poynting vector equation just today, so very timely. As its fresh in my mind, I found it remarkable that the magnetic and electric fields in an electromagnetic wave have exactly the same energy density as well.

9. Feb 9, 2010

### diagopod

Re: Is a changing B-field identical to a changing E-field in an electromagnetic wave

Thanks. Your explanation helps a great deal. Btw, I read tonight that the B field is simply the E field divided by C, at least in the context of an e.m. wave, which helps me get a sense of the seemingly total symmetry between the two as shown in those transverse-wave diagrams. Does that equation (E=BC and B = E/C) still hold outside of the context of an e.m. wave?

10. Feb 9, 2010

### bjacoby

Re: Is a changing B-field identical to a changing E-field in an electromagnetic wave

There are certain ideas you need to get crystal clear. The first is that E and B fields are not the "same thing" as is the current fashion to decree. They have different properties and even though in different reference frames they measure different values, since there is basically zero theory as to what they fields actually are in reality, it is WAY too early to proclaim them the same thing!

The next is that E and B fields DO NOT "create each other" either in electromagnetic radiation nor elsewhere. For example in induction (Faraday's law) it is usually assumed that a changing B field creates an E field. That idea is completely wrong. In electromagnetic plane waves a cursory look at the usual form of Maxwell's equations leads to the conclusion you expressed that E and B fields "create each other". As pointed out, that idea is also completely wrong. The truth is that the usual form of Maxwell's equations are NOT causal. Yes, the two fields are RELATED to each other, but they do not CAUSE each other.

What happens is that the primary source of BOTH the E and B fields is charge! As noted above, the Jefimenko equations give the causal relationship between charge, it's changes and both fields.

Hence in the case of induction it is a changing current (charge) that creates BOTH the changing magnetic field observed as well as the E field inducing potential in say a wire. In the case of EM waves, it is an accelerated charge that sends out into space BOTH a magnetic and electric field propagating away that are IN PHASE and just doing their thing. They are NOT creating each other! That is an idea that comes from misapplication of the ideas of energy exchange in an LRC circuit.

The key to a lot of this can be found by a closer look at the vector magnetic potential. Good luck!

11. Feb 9, 2010

### Born2bwire

Re: Is a changing B-field identical to a changing E-field in an electromagnetic wave

It could work out that way, but that is only valid in a source-free vacuum. Once you have a material with non-unity permittivity and/or permeability then the wave velocity changes. In addition, the transverse fields are not guaranteed if you have sources or confinement of the waves.

12. Feb 9, 2010

### diagopod

Re: Is a changing B-field identical to a changing E-field in an electromagnetic wave

This is the first time I've heard this. This actually makes more sense to me than a causal approach, since the orthogonal waves are perfectly in phase, neither one leading the other. I'll have a look at the resources you suggest as well. Thank you for all your help.

13. Feb 9, 2010

### diagopod

Re: Is a changing B-field identical to a changing E-field in an electromagnetic wave

Thanks Born2bwire, I'll try to keep this vacuum vs. material distinction in mind as I learn more.