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1. The problem statement, all variables and given/known data

You have a wire running along the z axis with radius a, a hole is drilled in this wire, off-centre, but also in the z-direction. The centre of the hole is distance d from the centre of the wire, it has radius b. There is also uniform current density in the wire, J.

I need to find the magnetic field, B at the centre of the wire

2. Relevant equations

[tex]\oint[/tex]B.dl=[tex]\mu[/tex]_{0}[tex]I[/tex]

3. The attempt at a solution

What I did initially is to split the wire into 3 sections. An inner cylinder, with nothing cut out of it, an middle ring which has the 'hole' drilled out of it, and an outer ring which has nothing cut out.

Since the inner cylinder and outer ring are entirely symmetric about the centre of the wire they contribute no magnetic field. (correct?)

you are left with a ring with a circular hole in it: http://s713.photobucket.com/albums/ww140/doive_photo/?action=view¤t=wire.jpg

(image seems to be broken so here's a link)

now i can work out the area of that easily so can find the enclosed current, but i'm stuck at what to do from this point? I just can't seem to come up with any sensible expression with that line integral?

EDIT: i'm also quite new to tex... so apologies for the dodgy formatting

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# Homework Help: Magnetic field within holey wire

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