Now the sheet of current has become a thick SLAB of current. The slab is infinit

Question

Now the sheet of current has become a thick SLAB of current. The slab is infinite in (both) x and y, but finite in z. So we must think about the volume current density J, rather than K. The slab has thickness 2h (It runs from z = -h to z = +h). Let's assume that the current is still flowing in the +x direction, and is uniform in the x and y dimensions, but now J depends on height linearly, i.e. J = J_0 |z| x inside the slab (but is 0 above and below the slab). Find B (magnitude and direction) everywhere in space (above, below, and also, most interesting, inside the slab).

Explanation / Answer

By amperes law,

integral Bdr = uo i enclosed

Lets take a amperes rectangle in yz plane symmetrical to both side of origin.

B*2y = 2uo* integral Jy dz

B*2y = 2uo yJo integral zdz

B = uoJo z^2/2....for |z| <h (inside the slab)

B = uoJoh^2/2 for |z| > h (above and below the slab)

  

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