20071119, 11:04  #1 
Apr 2004
Copenhagen, Denmark
2^{2}×29 Posts 
Formula split up
I'm doing a paper on the Hodge theorem and as part of this, I'm reading an article that presents the ideas of Hodge decomposition in the special case of domains in with a smooth boundary.
In order to prove certain propositions, the author uses the results from electrodynamics about how the magnetic field from a current distribution looks like. The way he presents the Maxwell law is a bit puzzling to me. The way I'm used to see Maxwell's law is but the author uses a slightly different version. He writes: where BS(V)(y) is the magnetic field from a current flow V, at the position y, is our domain with smooth boundary, is the closure of , means differentiation w.r.t. x (and likewise for y), and n is a boundary unit normal vector. Now to my question: It is clear that the term coming from a changing electric field has been broken into two parts: a part that accounts for that which happens 'inside' the domain and a part that accounts for that which happens at the boundary of the domain. Is this a purely mathematical trick that you could do with any vector field, or is there some physics at heart of this that allows the author to do this? Any hints as to how this split up is done would be greatly appreciated, as is a literature reference.  Best regards, Jes 
20071120, 11:42  #2 
"Lucan"
Dec 2006
England
14512_{8} Posts 
The printing is clear for me too. But who in their
right mind would use "V" to denote current??? 
20071120, 13:30  #3 
"Lucan"
Dec 2006
England
2·3·13·83 Posts 

20071120, 14:55  #4 
Apr 2004
Copenhagen, Denmark
116_{10} Posts 

20071120, 15:02  #5 
"Lucan"
Dec 2006
England
14512_{8} Posts 
THX for the explanation. But in my book V = "potential" (voltage)
Last fiddled with by davieddy on 20071120 at 15:03 
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