Okay - that eases thing up a bit :)
Use Ampéres law for the H-field:
\oint_{\partial \mathcal{S}}\vec H \cdot d\vec \ell = \int_{\mathcal{S}}\vec J_\mathrm{free}\cdot d\vec a
For points outside the wire, this of course reduces to the familiar form:
\oint_{\partial \mathcal{S}}\vec H \cdot d\vec \ell = I_\mathrm{free,encl}
but for points inside the wire, you must be careful to only include the part of the current that is enclosed by the loop - assume that the current density is uniform, if not stated otherwise.
THen you should find:
H\cdot2\pi r = J_0 \pi r^2 \quad\Rightarrow\quad H=\frac{J_0 r}{2} for r < 17.5 cm
Where J0 is the totalt current divided by the crossectional area of the wire
(take a moment to verify this)
Now use
\vec B = \mu_0(\vec M + \vec H)
together with
\vec M = \chi \vec H
to find the required result
