ABSTRACT
Consequently, the integral of —j • E over the magnetizing body gives the net power
P it produces, and the integral of i • e over the magnetizing body in (4.2), moved to
the other side of the equation, is just the net power P supplied by the magnetizing
circuit, and
P = f \ • edV + —— f (b2 + e2)dV (4.3) Jv 8jt 9/ Jas
For a cyclic state the integral of P over a time cycle is the net work done per cycle,
and according to Section 1.10 the loss per cycle is
4.3. The Macroscopic Applied Field Loss
In a similar way, forming the scalar product of (3.6) with H , and the scalar product
of (3.17) with E , and subtracting the two expressions leads to (in Gaussian units)
4TTJ E + H B + E D = - c d i v E x H (4.5)
Dividing the first term on the left into two parts as in (4.2) and integrating over all
space leads to
P = f j EdV + — I ( H B + E D)dV (4.6) Jv 4TT Ja 5,
Finally, with the use of (3.14) and (3.15) one obtains after an integral over a time
cycle
Q = j)di j i-EdV + <j)dt j ( H • M + E • P)dV (4.7) for the loss per cycle. Since the evaluation of the work done by the magnetizing
circuit is independent of whether one uses the Maxwel l -Loren tz or the Maxwel l
equations (4.7) and (4.4) give the same loss. However, (4.7) is usually much easier
to evaluate.
