• Support PF! Buy your school textbooks, materials and every day products Here!

Comprehending stated logical progression in thermodynamics

  • #1
10
0

Homework Statement


The idea is to describe work with a magnetized body within a solenoid. You have the equation of energy with field H by 1/8π∫H2dV where H=hi and h is a vector function of position.

Then you have if the work is changed dW/dt=d/dt[1/8π∫H2dV]

Then there is work in the creation of an elementary dipole within the body dm. the dipole has electron loop with current i' and area a, and the solenoid produces field h at the loop. If i' changes, the e.m.f. generated in solenoid is (h⋅a)di'/dt, so the battery must work at rate i(h⋅a)di'/dt.

Since solenoid field at loop is hi and by Ampere's theorem ai' is the magnetic moment:
dW/dt=H⋅dm/dt

Now here is where I start to get lost, but it kind of holds a little.
removing time derivatives and integrating over all space:
dW=d[1/8π∫H2dV] + ∫(H⋅dJ)dV

and here is where I get REALLY lost: where J is the intensity of magnetization (the magnetic moment dm of an element dV is JdV)

Can someone please explain that last step to me?
 

Answers and Replies

  • #2
18,079
7,499
Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

Related Threads on Comprehending stated logical progression in thermodynamics

  • Last Post
Replies
5
Views
624
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
0
Views
850
  • Last Post
Replies
0
Views
926
Replies
1
Views
6K
  • Last Post
Replies
5
Views
503
  • Last Post
Replies
2
Views
1K
Replies
6
Views
529
Top