Ampere's Law for current carrying wire

[btpolk]

Homework Statement

Use Ampere's Law to show that the equation for the magnetic field inside a current carrying wire is (1/2)μJr where J is the current density (assumed constant).

Homework Equations

∫B*ds=μI

The Attempt at a Solution

∫B*ds=μI

B*ds=B(ds)cosθ I think θ is 0 in this situation?

∫Bds=μI I believe r is length. If so would I=Jr?

∫Bds=μJr

From here I don't know what to do. What would my limits of integration be?

 

[tiny-tim]

hi btpolk!

I believe r is length. If so would I=Jr?

no, r is radius

and J is the current per cross-section area

 

[btpolk]

That said, I'm guessing I would treat the wire as a cylinder and the limits of integration would be 0 to 2pi? Also where does the J come in? Would it be some kind of substitution for I?