Magnetic field of an infinite layer

[Dell]

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

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 independent of z

 

[Andrew Mason]

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

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 independent of z

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 $\int B\cdot ds$ over the two sides of the rectangle in the z direction?

AM