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Electromagnetic wave and the phase between the E and B fields 
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#1
Jul1114, 05:30 AM

P: 54

http://www.physicsforums.com/showthr...00#post2881300
According to the quoted thread above and according to textbooks and Wikipedia the phase between the E and B fields of an electromagnetic wave propagating in free space is zero. This assertion is based on the Maxwell equations using a planar wave. DaleSpam rephrases Maxwell's laws in the quoted thread: ##∇ \times B=\frac{∂E}{∂t}##the curl of the magnetic field is then zero when the electric field is maximal or minimal. If the curl of the magnetic field is zero, then my interpretation of what the curl means, leads to the conclusion that the magnetic field itself has a zero value. To continue with this, when the electric field is zero, the rate of change of the electric field is maximal and the curl of the magnetic field is maximal too, which leads to the conclusion that when the electric field does not exist (its rate of change is maxed), the magnetic field magnitude is maximal and rotational. This goes against the interpretation of DaleSpam, which to me is solely based on a math interpretation, not a physical interpretation. I would conclude that there is a 90° phase difference and that therefore ##E=E_{0}sin(\omega t  kx)##is incompatible with the Maxwell equations. Of course I might be completely wrong, yet DaleSpam's explanation does not cut it for me, unless my interpretation of the curl of a vector field is out of touch. 


#2
Jul1114, 06:22 AM

Sci Advisor
Thanks
PF Gold
P: 1,908

For a correct analysis, please review http://www.phy.iitb.ac.in/~dkg/PH102/emw.pdf
The E and B fields are in phase. This is often used as a homework problem in your basic electromagnetic field theory course. 


#3
Jul1114, 06:53 AM

P: 54




#4
Jul1114, 07:53 AM

Sci Advisor
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P: 3,412

Electromagnetic wave and the phase between the E and B fields
That's the acid test for whether something is a valid solution for the equations. If you do that and you still find an incompatibility, show your work and one of us will be able to help you find the place where your calculation went astray. 


#5
Jul1114, 08:41 AM

Sci Advisor
Thanks
PF Gold
P: 1,908

You could try solving for spherical waves, and see what you get. 


#6
Jul1114, 08:51 AM

C. Spirit
Sci Advisor
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P: 5,401

Yes electric and magnetic fields can be out of phase e.g. if you consider certain superpositions of plane waves of certain polarizations: you can easily construct standing waves from superpositions of two oppositely propagating circularly polarized plane waves so as to have the electric and magnetic fields ##\pi/2## radians out of phase in time or space.



#7
Jul1114, 09:00 AM

P: 54

In my original post I am contesting the notion, the physical interpretation, the interpretation of a rotational field, DaleSpam gave in a previous thread. Again, is there a merit in saying that when the curl of a field is zero, that then the field it self is zero? If there is merit, I will try to come up with something that would make sense. Right now I do not see the point when I am wrong in how to interpret the curl of a field. 


#8
Jul1114, 09:08 AM

Mentor
P: 16,942

See here for an example of nonzero fields with zero curl. http://en.wikipedia.org/wiki/Conserv..._vector_fields Note, a plane wave is not irrotational everywhere, but where dE/dt=0 it is easy to show that ∇xB=0 also. 


#9
Jul1114, 09:15 AM

Mentor
P: 16,942




#10
Jul1114, 09:56 AM

Mentor
P: 11,593

$$\vec \nabla \times \vec B = \frac{1}{c^2} \frac{\partial \vec E}{\partial t}$$ 


#11
Jul1114, 11:36 AM

P: 54

An electromagnetic wave can be planar and circular polarized. A planar wave (polarized) can be decomposed into two dichroic circular waves. A circular wave (left or right) can be decomposed into two planar waves orthogonal to each other with a phase difference of ##\frac{\pi}{2}##. Each such planar wave can again be decomposed into dichroic circular waves, etc. Given the above, what will be the basic wave for a photon, circular, planar? Does a circular polarized wave has the the electric and magnetic fields in phase? 


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