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This isn't a homework question, just a curious question. I've been working on problems involving Ampere's Law and slabs of current density

**J**.

I've drawn a diagram to illustrate my question:

http://www.freeimagehosting.net/t748n

Here, two infinite slabs of current are placed one on top of the other, in the xz-plane. The magnitudes and directions of

**J**in and

**J**out are such that the magnetic field outside the slabs is zero (i.e.

**B**= 0 for y>d and y<-d). Also, I assume that the current densities vary with distance inside the slab (because if they didn't, I could simply take my entire Amperian loop inside of each slab centered on the middle of the slab). Therefore, if the current densities are functions of distance y, I have to hang my Amperian loop outside of the slabs where the magnetic field is zero.

I'm trying to use Ampere's Law to find the magnetic field

*inside*each slab (i.e. 0<y<d and -d<y<0). The textbook I've been working with (among other sources) draw the Amperian loops similar to loops 1 and 2 in the diagram. The red part of each loop is the part I'm solving for. Each of the other 3 segments either cancel by symmetry, or the field is zero along that path.

So here's where I'm confused: I don't understand why loops 1 and 2 are correct (or are they?). Loop 1 doesn't seem to account for the field produced by the bottom slab of current. It would make more sense (to me) if loops 3 and 4 were the correct loops. As loop 3 accounts for the field produced by the bottom slab, and loop 4 accounts for the field produced by the top slab. Can anyone explain this?

Thanks in advance!