So what is your question?
Are you being serious friend?
The thread is called ''Does an EM-Field contain a vorticity''?
I thought it says it on the tin, so-to-say.
So what is your question?
Are you being serious friend?
The thread is called ''Does an EM-Field contain a vorticity''?
I thought it says it on the tin, so-to-say.
Wikipedia said:The definition canonical momentum corresponding to the momentum operator of quantum mechanics when it interacts with the electromagnetic field is, using the principle of least coupling: $$\mathbf{P} = m\mathbf{v} + q\mathbf{A}$$ instead of the customary $$\mathbf p = m\mathbf{v}$$ where:
- $$\mathbf{A}$$ is the electromagnetic vector potential
- $${m}$$ the charged particle's invariant mass
- $$\mathbf{v}$$ its velocity
- $$q$$ its charge.
If you want to know if the EM field has vorticity, then just look at Maxwell equations.
The OP has nothing to do with this.
Why did you write the first post which is totally unrelated to the question?
Ah. As for the actual Wikipedia quote we have:
http://en.wikipedia.org/wiki/Momentum#Momentum_in_electromagnetism
The text was added in near its present form by user AndyWall on March 28, 2006, who does not have much physics content.
http://en.wikipedia.org/w/index.php?title=Momentum&action=historysubmit&diff=45866672&oldid=45835019
The text is still not proper English ("The definition canonical momentum " should properly read: "The definition of canonical momentum"), but the phrase "Canonical Momentum" is a term of art within the domain of Lagrangian mechanics and it is not obvious that this is correct or suitable for a general Wikipedia page on momentum, especially as the Lagrangian is not displayed or (as AlphaNumeric pointed out) a covariant one derived from modern treatments of electromagnetism.
See J.D. Jackson Classical Electrodynamics (1962) or similar for
$$p_\mu = \left( { E/c \\ \vec{p} } \right) = \left( { m \gamma c \\ m \gamma \vec{v} } \right) - q \left( { \phi \\ \vec{A} } \right) = m U_\mu - q A_\mu $$
(if I haven't left out any minus signs or factors of c)
http://sciforums.com/
I told you: look at Maxwell equation, you know curle(E) = ... etc.Point in the right direction then.
You said yourselfAnd the OP is very much to do with this. :bugeye:
A is the fieldExactly. It doesn't change A...
I told you: look at Maxwell equation, you know curle(E) = ... etc.
You said yourself
A is the field
By changing v into curl(v) you do not change the field.
Don't you see that this does not change/check the vorticity of the field.
By the way, when you write the cannonical momentum in the Hamiltonian, and writting down the Hamilton's equation of motion, you get the Lorentz force that act on the particle
But it is not because:If the equation is true.
Yes I know, his name is James Clerk Maxwell, he gave the evidence more than 100 years ago, there may be methods in detecting a vorticity of the EM field - as you will notice, it seems someone has provided evidence of this.
The momentum that you gave in the OP are not the field momentum. They are the momentum of a particle in the field.Now, 1102, you said maxwell has derived the properties I am seeking. If we use the definition of momentum above, how does the vorticity enter the equations?
As I said before, I have searched the net, and I found two equations supposidly describing the vorticity, but both of them looked very dubious.
I will add, I recognize that the equation in the OP is incorrect, so, I have studied on it more, hence why I am now referring to the equation in post 30.
So, I've been reading more. One can say the momentum density of the electromagnetic field as:
$$\vec{p}= \frac{1}{c^2} \vec{E} \times \vec{H}$$
Where $$p$$ is for momentum, E is the electric field and H is the auxilary magnetic field. One can clearly see how this is related to the Poyinting Vector.
In fact I knew that the Poynting vector was not named that way because it points to direction of energy flow (even though the name is appropriate), but after the name of the physicist. This is why I wrote it with a "yi", thinking that this is the correct spelling.The pedant in me is compelled to point (chuckle) out that the correct spelling is POYNTING vector. It's so called because it's named after John Henry Poynting, not because it points at anything.
One can clearly see how this is related to the Poyinting vector since This is the Poyinting vector.
Now, what has it to do with vorticity of the fields?
In which equation do you want to take the curl of the velocity?I could take the mathematical route and say that on the left-hand side of the equation could be modified to suit the curl of the velocity.
I bet there is a much more substantial and correct answer, which is were you come in.
I am reminded of Multitwist Optical Möbius Strips by Isaac Freund (Optics Letters Vol. 35, No. 2 January 15, 2010). A forked fringe is employed, and the vortices are caused by light. Here's a "fair use" extract from it:Did he ever come to a conclusion what caused the vortices? Did he even come to a conclusion what effect this has one particles, or maybe perhaps better worded, what attributes particles have which can be explained by vortices in the electromagnetic field?