| Topic: |
Science > Physics |
| User: |
"rancid moth" |
| Date: |
04 Oct 2005 01:29:58 AM |
| Object: |
Energy density of electric field |
hello,
The energy density of the electric field is given by
u = 1/2 (E^2)
setting permitivity*dielectric constant = 1
if we were in two dimensions and the electric field had two vectorial
componants E1 and E2 one has
u = 1/2 (E1^2 + E2^2)
one may write this as
u = 1/2 (E1+iE2)*(E1-iE2)
i=sqrt(-1) does anyone know of any source that discusses the quantity
(E1+iE2), or uses this decomposition?
cheers
moth
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| User: "Rusty" |
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| Title: Re: Energy density of electric field |
04 Oct 2005 02:41:33 AM |
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"rancid moth" <rancidmoth@yahoo.com> wrote in message
news:dht7hv$f0r$1@news-01.bur.connect.com.au...
hello,
The energy density of the electric field is given by
u = 1/2 (E^2)
setting permitivity*dielectric constant = 1
if we were in two dimensions and the electric field had two vectorial
componants E1 and E2 one has
u = 1/2 (E1^2 + E2^2)
one may write this as
u = 1/2 (E1+iE2)*(E1-iE2)
i=sqrt(-1) does anyone know of any source that discusses the quantity
(E1+iE2), or uses this decomposition?
Yes, this is the Stokes decomposition of a vector field.
http://scienceworld.wolfram.com/physics/StokesVector.html
which you have rediscovered independently.
rusty
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| User: "rancid moth" |
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| Title: Re: Energy density of electric field |
05 Oct 2005 01:16:29 AM |
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[snip]
Yes, this is the Stokes decomposition of a vector field.
http://scienceworld.wolfram.com/physics/StokesVector.html
which you have rediscovered independently.
rusty
I had a look at that link though couldnt see anything that relates it back
to a more general problem other than polarization and electric fields that
are wave like. Further investigation lead me to fluid mechanics and complex
analysis namley the description of EM or fluid mechanics problems in terms
of stream functions, which is exactly what E1+iE2 represents.
cheers
moth
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