Derivation of the coupling effect

[ms]

Here is a derivation of the coupling of a pickup to another inductor like thing that I did a few years ago. The algebra is not so complicated, and I consider several limiting case to demonstrate that it makes sense, and then show the results in several forms.  I have attached a png file for each page since I cannot figure out how to attach a multipage pdf file.

Edit: The pages can be blown up by putting them in another viewer if your browser cannot do it directly.

[stratotarts]

I have the PDF file. You must have posted it somewhere else.

[ms]

This downloads  it:

www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=2ahUKEwiy2eDhkazfAhUOjlkKHQFiAmwQFjAAegQIABAB&url=http%3A%2F%2Fmusic-electronics-forum.com%2Fattachments%2F26471d1385509250-mutualinductanceloading.pdf&usg=AOvVaw32OhzrGmMHUeREXmaESFnN