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Magnetic Field of a Thin Conducting Plate

  1. Mar 18, 2012 #1
    A very, large, thin conducting plate lies in the x-y plane. The plate carries a current in the y direction. The current is uniformly distributed over the plate with σ amperes flowing across each meter of length perpendicular to the current. Use Ampere's Law to find the magnetic field at some distance from the plate. (Hint: The magnetic field lines are parallel to the plate.)

    2. Relevant equations
    Ampere's Law:
    ∫B|| ds = μ0*I

    3. The attempt at a solution:
    I'm completely lost on where to even start this question. I guess that you may have to use a Gausian cylinder or rectangular prism.
     
  2. jcsd
  3. Mar 18, 2012 #2

    Redbelly98

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    Welcome to PF!

    For Ampere's Law, instead of a surface you are looking for a closed loop to draw somewhere. In general, the geometry of the problem might suggest some simple shape -- often a circle or rectangle -- that will make things work out.
     
  4. Mar 18, 2012 #3
    So if I use a rectangular wire around the plate, do I only include the top and bottom portions of the length, since these are the only sections where the B is perpendicular to the path?

    Also how do I calculate the current, is it just equal to σ?
     
  5. Mar 19, 2012 #4

    Redbelly98

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    Yes, use a rectangular path. But have a look again at Ampere's Law, you are looking for sections where B is parallel to the path:
    "B||" means the component of B that is parallel to the the length element ds.

    σ is the current in 1 meter of plate. So if the rectangle encloses 1 meter of the plate, yes. If the rectangle encloses some other length, then no.

    Have you drawn the rectangular loop yet? The thin plate should appear as a line in the figure, with the current directed either out of or into the page.
     
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