A A derivation in Stoner's "The Demagnetizing Factors for Ellipsoids"

[MathematicalPhysicist]

In the attachment in eq. (1.6) I don't understand why is $H-B = B/(1-D)$?

Where does this relation come from?

 

[Charles Link]

$H=-D(B-H)$. They got that part right. Let's do some algebra: $H(1-D)=-DB$, so that $H=\frac{-DB}{1-D}$. Their last equation of 1.6 needs a minus sign. $\\$ Note: Equation 1.6 assumes the applied magnetic field $H_a$ is zero. $\\$ And I also checked equation 1.7, and it is correct.

 

[MathematicalPhysicist]

To tell you the truth I wasn't sure it's implied from the same relation in (1.6).
I thought to myself that it was some relation from previous work or somewhere else in the article.

Now that I see that's a simple matter of algebra I feel so stupid... D-:

 

[Charles Link]

The author did have a "typo" in equation 1.6 (missing the minus sign). I'm glad you posted it. IMO more people should be studying E&M concepts such as the demagnetizing factor. We could use more E&M postings.

 

[MathematicalPhysicist]

I kept on reading the paper.
On page 11 in the following attachment in eq. (4.11a) for $D_a$ after the first equality should it be $3/4\mu^4 \ln (2m)$ or as it is written there?
I am asking since after the second equality they write it as $3/4 \mu^4 \ln (2m)$.

 

[Charles Link]

It looks to me like it should be 3/2, but I would have to see the previous page. Clearly they have an inconsistency there.

 

[MathematicalPhysicist]

It isn't discussed in the previous page.

You can find the article in sci-hub. (I know it's not really legal, but also making ordinary people who are interested in science pay lots of money for papers in science is a rip off).

 

[MathematicalPhysicist]

It looks to me like it should be 3/2, but I would have to see the previous page. Clearly they have an inconsistency there.

Hi @Charles Link have you kept on reading this article, perhaps?

I plan to return to Ashcroft and Mermin and Kittel's books once more for my Condensed Matter Physics I, hopefully now I will ace it in this summer!

 

[Charles Link]

Hi @Charles Link have you kept on reading this article, perhaps?

No, I didn't do any additional reading of it.