Conducting Wire Homework: Find J0 & B Inside Wire

[dtesselstrom]

Homework Statement

A long, straight conducting wire of radius R has a nonuniform current density J=J0*r/R, where J0 is a constant. The wire carries total current I.
Find an expression for J_0 in terms of I and R.
Find an expression for the magnetic field strength inside the wire at radius r.

Homework Equations

J=I/A
B*ds = u0*I

The Attempt at a Solution

So from my book it looks like J0=I/A which is Jo=I/(pi*R^2) which says it is off by a multiplication factor not sure where I am going wrong here. As for the second portion I got B= uo*I*r/(2*pi*R^2) which is also wrong so any help on this would be much helpful.

 

[robb_]

Since J is a function of r, it will be constant for a thin cylindrical shell centered on the wire. Adding up the current in all these shells will equal I.