How Do You Calculate Magnetization in an Iron Alloy Solenoid?

[howdoIphysics]

Hey I'm new here so I don't know if this is the right forum, but from what I could see this was the most relevant.

Homework Statement

A long solenoid with 50 turns per cm carries a current of 0.2 A. The solenoid is filled with an iron
alloy. The magnetic field B inside the iron alloy is measured to be 1.58 T acting parallel to the axis of
the solenoid.

Calculate the:
i) size of the applied field Bapp;
ii) size of the magnetization M in the iron alloy;

Homework Equations

This is my problem really as I don't know so far I've been using the magnetic field of a solenoid = (N/L)
*I*μ₀, however I don't know if this correct or if it needs the permeability of the core to produce an accurate value.
I've also been using B_t= B_app+μ₀*M rearranged to M= (B_t-B_app)/μ₀ to answer the second question.

The Attempt at a Solution

Well this is just plugging numbers into the equations so I'm confident that I haven't done anything wrong here.
Assuming the solenoid field is B_app, B_app=5000*0.2*1.3×10⁻⁶ = 0.0013.
Putting that into the rearranged equation. M = (1.58 - 0.0013)/1.3×10⁻⁶ = 1.210⁶.

My problem here is those values seem very small and ridiculously large respectively, have I done something wrong or am looking for errors where there are none?

 

[BruceW]

hey, welcome to physicsforums! uh, your answers look good to me. Although when you hand in your work, you should probably give units, and maybe be a bit more careful on the rounding-off. But it's essentially good. And yes, one is very large and the other is very small. But this is just because SI units are like that. Looking at your equation M= (B_t-B_app)/μ₀ And since μ₀ is very small in SI units, the ratio between B_t-B_app and M will always be an 'extreme' ratio, in SI units.