How to Calculate Work of Isothermal Magnetization?

[TristanJones]

Homework Statement

A magnetic salt obeys the Curie Law
μoM/Bo = C/T
Where M is the magnetization, Bo is the applied magnetic field in the absence of the specimen, C is a constant, and μo is the permeability of free space. The salt is magnetized isothermally from a magnetization M1 to M2. You may assume that the magnetization is uniform over the volume V of the salt. Show that the work of magnetization is:
W = VμoT(M2²-M1²)/2C

Homework Equations

W = --∫Hdm, from M1 to M2. H= MT/C

The Attempt at a Solution

To start, I use W = -∫Hdm, from M1 to M2. using H = MT/C and integrating, I end up with W = -T(M2²-M1²)/2C. How do I also get μo and V in the numerator, as well as removing the negative sign? What am I missing here?
(not necessarily looking for a blatant answer so much as a nudge in the right direction.)

Cheers.

 

[TSny]

Homework Equations

W = --∫Hdm, from M1 to M2.

Are you sure that this equation shouldn't also include μ₀ and V?
When written with the negative sign as you did above, does this equation represent the work done by the system or the work done on the system?

 

[TristanJones]

I'm using an equation provided in my notes. If the equation is supposed to already include V and μ0 then... well, that would be great, but I need the basis for it, which I'm having trouble figuring out.

And with the negative sign, I think it represents the work performed by the material itself, so perhaps I should treat it as external instead?

 

[TSny]

https://books.google.com/books?id=r...ne magnetization constant temperature&f=false

 

[TristanJones]

well, I guess that answers it! I must've been interpreting what the question was asking incorrectly and using an incorrect formula. the one described in that link fits this much better, I think.

 

[TSny]

Your notes might have been dealing with the work per unit volume. But, still, it should have had the μ₀ if working in the SI system. The wording of the problem is not very clear about whether they are asking for work done on the system or by the system.