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the surfaces r = 1cm and r = 4cm and the planes z = 0 cm and z = 2 cm, and the surface

current density on the surface defined by r = 4cm is given by -60az A/m.

(a)

Specify the current densities on the surfaces at r = 1, z = 0, and z = 2.

(b)

Find the expression for H inside the toroid (i.e. in the region 1 < r < 4 cm and 0 <

z < 2cm).

I have the solution, I just don't really understand it. The current density, K, for r=1 was found to be 240 A/m.

To find the field inside the toroid ampere's law is used [itex]\oint[/itex]H dl = 2∏r = ∫K

_{r=1}dθ from θ=0 to 2∏. Giving the final answer of H=15/(2∏r)

So in this question K is different at r=4 and r=1. Is it changing due to distance from the sources of the field, or is it uniform and I'm missing some simple math? Since K is different at different radii, how come we integrate only integrate with K

_{r=1}and not other any other K's? I mean it is changing and I'm assuming since the cross section of the toroid is a square loop, all four sides would contribute to the field inside the toroid, not just r=1 .

Wouldn't I need to calculate for K

_{r=4 }and K

_{z=0}=K

_{z=2}and sum them up? Hope that made sense, thanks in advance.