# Magnetization of water surrounding submerged non-magnetic wire

1. Nov 3, 2013

### GoliathPSU

1. The problem statement, all variables and given/known data
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 χm. What is the bound current density Jb(r) for s > R. Calculate the total current (free plus bound).

2. Relevant equations
H = $\frac{1}{\mu0}$B - M
$\oint$B $\bullet$ dl = $\mu$0Ienc
$\oint$H $\bullet$ dl = If, enc
M = $\chi$mH
Jb = ∇ × M

3. 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.

2. Nov 3, 2013

### 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.