Document 2669842

continuing Chapter 12 ...
(1) Magnetic Force and (2) Inductance
Theorem. The total energy of a
magnetostatic system is
1
UB = 2μ
0
Proof.
∫ B2 d3r
(1)
Calculate the energy required to change a
system of currents.
The change of energy is equal to the work done
by the external forces, which is equal to (-1)* the
energy done by the fields.
Proof.
Corollary . The total energy of a
magnetostatic system is
UB = μ0 ∫ j(r)∙j(r’) d3r d3r’
(2)
8π
| r − r’ |
“Potential energy” for current loops
(Zangwill, Section 12.7)
Consider a system of current loops.
Ik = the current in a current loop;
Rk = center of mass of the current loop
Define a function
^
^
UB = U B ( I 1 I 2 … I N ; R1 R2 … RN )
Inductance
(The flux is independent
of which Sk is used.)
2
2
C1 = Ci
C2 = Ck
Homework Assignment 4
problems from chapter 12
due Friday Sept 26
12.3
12.7
12.11
12.20
12.21
12.22