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Magnetic field of an infinite layer

  1. Jun 8, 2009 #1
    given a n infinite layer, with a thickness of D and a current density of J direction in the diagram (on x-), prove that the magnetic field above the layer is constant irrespective of the height 'z'

    http://lh4.ggpht.com/_H4Iz7SmBrbk/Si1JMFGiWEI/AAAAAAAABEE/LVo64TBgsmw/Untitled.jpg [Broken]

    i had a similar problem in electrostatics and what i did was use gauss law, here what i want to do is use amperes law, the problew is finding the correct path to use. i think that it must be a rectangle path therefore my closed integration will be in 4 parts, 2 along the y axis, 2 along the z axis,, i thought of taking a path of length L, at a height Z,

    somehow i need to get 0 for the integration of the heights, so that my equation is independant of z
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jun 9, 2009 #2

    Andrew Mason

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    Take any rectangular path enclosing the full thickness of a section of the slab that is in the yz plane.

    By symmetry, what can you say about the component of B in the z direction? What does this say about [itex]\int B\cdot ds[/itex] over the two sides of the rectangle in the z direction?

    AM
     
    Last edited by a moderator: May 4, 2017
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