Re: Electromagnetic stress-energy tensor :)
- From: dubious@xxxxxxxxxxxxxxxxxxxxxxxxxxxx (Bilge)
- Date: Wed, 31 Aug 2005 06:46:10 GMT
Lacustral:
>So I've been reading about the stress-energy tensor. I don't understand the
>stress-energy tensor for the electromagnetic field.
>
>The book says the space-space components of the stress tensor describe a
>tension (E^2 + B^2)/8pi along the field lines.
>And a pressure (E^2 + B^2)/8pi perpendicular to the field lines.
>
>What the space-space components of it look like, is:
>
>T^jk = 1/4pi ( -(E^j*E^k + B^j*B^k)) + 1/8pi (E^2 + B^2)*I
>
>where I is the identity matrix.
>
>I can see how there is a pressure (E^2 + B^2)/8pi in the E x B direction -
>since E x B would be in the null space of the E^j*E^k + B^j*B^k matrix.
I'm not quite sure I understand what you're asking. Are you asking
how to derive that expression above or are you asking how to express
it using some particular terminology?
>
>But I don't see where there's a tension (E^2 + B^2)/8pi along
>the field lines.
>The E^j*E^k + B^j*B^k matrix does map the (E,B) plane into itself. But
>neither E or B are necessarily eigenvectors of this matrix. It would have
>real eigenvalues because it's symmetric, but the eigenvalues don't seem to
>be E^2 + B^2, either.
>
>So I don't get it. Can some kind person explain this?
>
>Laura
.
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- Electromagnetic stress-energy tensor :)
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