Poynting vector. Conservation theorem.

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SUMMARY

The discussion centers on the Poynting vector and its relation to the conservation theorem in electromagnetic fields. The user calculates the electric field (E) and finds the magnetic field (B) to be zero, leading to a Poynting vector (S) of zero. This indicates that the field is static and does not transfer energy. The user struggles with verifying the conservation theorem, specifically grad(S) + de/dt = 0, outside the particle's trajectory, and questions the significance of this condition.

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  • Study the implications of energy conservation in electromagnetic systems
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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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