Magnetization of water surrounding submerged non-magnetic wire

[GoliathPSU]

Homework Statement

A long straight wire of circular cross section with radius R carries current I and is immersed
in a large volume of water. The wire is non-magnetic. Calculate the magnetization M(r) in
the water which has a susceptibility χ_m. What is the bound current density J_b(r) for s > R. Calculate the total current (free plus bound).

Homework Equations

H = \frac{1}{\mu₀}B - M
\ointB \bullet dl = \mu₀I_enc
\ointH \bullet dl = I_{f, enc}
M = \chi_mH
J_b = ∇ × M

The Attempt at a Solution

This is how I am thinking about it... the magnetization in the water arises from the current (and resultant B-field) carried by the wire, so I feel like I should calculate the B-field cause by the wire with Ampere's law but then I am unsure of how to use that to find the magnetization in the water.

 

[TSny]

Hello, GoliathPSU. Welcome to PF!

Start by finding an expression for H outside the wire as a function of the distance r from the central axis of the wire.