Question

A wire of radius R carries a non-uniform current: the current density, j, (current per unit area) varies as a function of distance r from the central axis of the wire according to j = j0(R/r) (and j = 0 outside the wire, of course). Find expressions for the strength of the magnetic field in the regions 0 < r < R and R < r.

Answer 1

Use Ampère's law:

http://en.wikipedia.org/wiki/Amp%C3%A8re's_circuital_law

2 pi r B(r) =

Integral from r' = 0 to r of

2 pi r' j(r') dr

Answer 2

Typo:


2 pi r B(r) =

µ_0 Integral from r' = 0 to r of

2 pi r' j(r') dr