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When we say current, I, through a wire is uniform, what do we mean?

  1. Aug 7, 2007 #1
    when we say the current through a wire is uniform and is [tex]I[/tex] what do we mean
     
    Last edited: Aug 7, 2007
  2. jcsd
  3. Aug 7, 2007 #2

    chroot

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    Consider the circular cross-section of the wire. Now consider just the top half-circle, and the bottom half-circle.

    If the current is uniformly distributed through the wire, then the current through each of these half-circles is the same: I/2.

    Generally, if the current is uniformly distributed through the wire, the any two regions of the cross-section with the same area will be carrying the same current.

    - Warren
     
  4. Aug 7, 2007 #3
    and does the current is i mean the current through the cross section perpendicular to current flow
     
  5. Aug 7, 2007 #4

    chroot

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    Usually, yes.

    - Warren
     
  6. Aug 7, 2007 #5
    ok two more.
    how do u define surface current density
    also when we say in cas eof steady current the current through the wire is i what do we mean
     
  7. Aug 7, 2007 #6

    olgranpappy

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    The answers to the question of definition can be found in any textbook. I would suggest that you look in the appendix of Griffith's--maybe under "surface current" or "current, surface"?
     
  8. Aug 8, 2007 #7
    i am asking u after reading from griffith :biggrin:
     
  9. Aug 8, 2007 #8

    jtbell

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    How does Griffith define surface current density and what, specifically, don't you understand about that definition?
     
    Last edited: Aug 8, 2007
  10. Aug 8, 2007 #9
    well he says and i quote
    well what i don't understand about this is why should we take a 'ribbon' isn't a small width enough to define .also if a take a width then the current flowing across it in general would depend on the ribbon length
     
  11. Aug 8, 2007 #10

    Meir Achuz

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    Surface current denslity is current per unit width of Griffith's ribbon, so
    K times the width is the current.
     
  12. Aug 8, 2007 #11

    Meir Achuz

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    A somewhat more mathematical definition of surface current density is
    "The surface current density is defined so that the current flowing past a differential line element
    [tex]{\vec dL}[/tex] on the surface is given by
    [tex]
    dI={\vec K}\cdot({\vec dL}\times{\vec n})[/tex],
    where [tex]{\vec n}[/tex] is a unit vector normal to the surface."
     
  13. Aug 8, 2007 #12
    but since the ribbon has length and we have taken it along the flow of current won't the current depend on length of ribbon
     
  14. Aug 8, 2007 #13

    olgranpappy

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    The ribbon is introduced for visualization purposes. the surface current density is a local property and doesn't depend on any "ribbon" or "ribbon length" introduced as a pedogogical aid.

    The surface currect density is a vector in the plane of the surface and in the direction of the current flow at a point. It's magnitude is proportional to the strength of the current I at the point.

    If you integrate the surface current density along some line [tex]\vec \ell(s)[/tex] embedded in the surface (here my line is parametrized by the real number [tex]s[/tex]) you get the current flowing across that line:
    [tex]
    I_{\textrm{across line}}=\int d|\ell|\hat t\cdot \vec K
    [/tex]
    where [tex]\hat t[/tex] is the one of the two unit vectors perpendicular to [tex]\frac{d\vec \ell}{ds}[/tex] whose angle with [tex]\vec K[/tex] is smallest.
     
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