Poynting vector. Conservation theorem.

AI Thread Summary
The discussion revolves around calculating electric and magnetic fields, specifically focusing on the Poynting vector and the conservation theorem. The user finds that the magnetic field B is zero, leading to a Poynting vector S of zero, raising questions about its significance. They also struggle with verifying the conservation theorem, particularly in regions outside the particle's trajectory, where they assume no charges are present. The consensus is that the static nature of the fields implies no energy transfer, suggesting the user may need to reassess their expressions for the electric and magnetic fields. The conversation emphasizes the importance of understanding field behavior in relation to energy conservation.
lailola
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I'm doing a problem where I have to calculate the electric and magnetic fields. I've found B=0, so S=ExB=0. Has it got any meaning?

Then I calculate the energy density e=E^2 + B^2 = E^2. And finally I have to verify the conservation theorem grad(S)+de/dt=0 for points out of the particle's trayectory. I do this part but the conservation theorem is not satisfied. What is the significance of "out of the particle's trayectory"? Or maybe I've got wrong expressions for E and B...

Thanks.
 
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Has it got any meaning?
Your field is static and does not transfer energy.

What is the significance of "out of the particle's trayectory"?
You can assume that there are no charges in the (infinitesimal) volume where you verify the relation.
 
mfb said:
Your field is static and does not transfer energy.


You can assume that there are no charges in the (infinitesimal) volume where you verify the relation.

So, when I do the time derivative of the energy density it must be zero. Then, I think I haven't got the correct expressions for the fields.

Thanks a lot for your help!
 

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