ABSTRACT
Consider the approximate set of Maxwel l equations (in SI units, where a dot is
used for the time derivative)
c u r l E = - B (5.1)
c u r l H = j (5.2)
d i v B = 0 (5.3)
d i v E = 0 (5.4)
which are solved with the approximate constitutive equations
B = MOH (5.5)
and E
j = Jc-(5.6) E
with jc taken to be a constant. Eq . (5.6) applies for E 0. If E is always along
the z axis and z is a unit vector in the z direction, then
and for E = 0
J ±y ' c z for the cyclic slate (5.8)
0 for the virgin state (5.9)
depending upon the magnetic history. Assuming a uniform applied field H„ in the
plane of the sheet along the x axis, one may expect H to be along this axis and to
be function only of y [see Figure 5.2(a)]. The current density j also varies with y
through the thickness of the sheet, taking one of the values ± jc or 0 at any point
but, in a piecewise-sense, j is constant. The solution of Eqs. (5.2) and (5.3) is
H = ( C - ; y ) x (5.10)
where C depends only on time. Since
H = Cx (5.11)
the time derivative of H is a piecewise constant in space, and the solution of (5.1)
and (5.4) for the electric field is
E = (K - /.i0Cy)z (5.12)
Figure 5.2 (a) Section of a sheet with field applied along x axis and transport current flowing along ; axis, (b) Current distribution, with the dashed lines representing moving boundaries. An initial flux-free state is assumed, (c) Electric and magnetic fields.
