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Homework Help: K, the idealized surface current density

  1. Jul 7, 2005 #1
    K, the "idealized surface current density"

    Hey, I don't quite understand that guy, K.

    I have an exam on Sunday in E&M, I'm studying from Jackson. I haven't found any definition of 'K'.

    If anyone could give me a rigurous definition and an integral form, if there's any, I'd appreciate it.
    Oh, and since we're at it, I stumped into that next statement:
    "Suppose that the upper half of space is filled with a permeable media, while the other half is empty space. If, in the x-y plane, K is in the x direction, it follows that A (vector potential) is also in that direction in the entire space".
    Huh?
     
  2. jcsd
  3. Jul 7, 2005 #2

    quasar987

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    What definition do you have so far with which you are unsatisfied?

    Griffiths (pp.211) gives the following definition: "When charge flows over a surface, we describe it by the surface current density K, defined as follows: Consider a "ribbon" of infinitesimal width [itex]dl_\perp[/itex], running parallel to the flow. If the current in this ribbon is [itex]d\vec{I}[/itex], the surface current density is

    [tex]\vec{K}=\frac{d\vec{I}}{dl_\perp}[/tex]

    In words, K is the current per unit width-perpendicular -to-flow. In particular, if the (mobile) surface charge density is [itex]\sigma[/itex] and the velocity is [itex]\vec{v}[/itex], then

    [tex]\vec{K}=\sigma \vec{v}[/tex]"

    It is not written but I believe we can write the integral form as

    [tex]I_{surface} = \int_{\mathcal{P}}\vec{K}\cdot d\vec{l}[/tex]

    where [itex]\mathcal{P}[/itex] is a path across the surface.
     
    Last edited by a moderator: Mar 29, 2014
  4. Jul 7, 2005 #3
    Thanks.
    But then, in the statement I gave, why is A in the x direction? I just can't see it.
     
  5. Jul 7, 2005 #4

    quasar987

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    I don't know what permeable means, I'll have to leave that one to someone else.
     
  6. Jul 7, 2005 #5
    It may not be the right term. It simply means it's a linear matter for some 'miu'.
     
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