Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

The e1ectrica:L effect - of the changes is vel?y important. They modify
by a-ttraction and repulsion .the 'curren-t flow; in particul.ar surface
changes deflec-t the current lines in such a way tllat the norinal
current coriiponent vanishes a-t the surface. Iil con-tras-t the magnetj-c -
effect i.s of the ordel- of that of the disp1acemel-i-t current and
can be neglected.
2. E1ectromagneti.c induction in I-di.mensiona1 structures
2.1. The q,eneral solution
The following vector analytical. identities are used in the sequel
(A
- is a vector, $ a scalar).
div curl - A = 0
(2.1)
curl grad + = 0 (2.2)
div(A+) - = @ div - A -1. & a grad 41 (2.3)
curlCA+) -- = + curlA - Ax - grad @ (2.4)
curl"+ - = grad divA - - AA - (2.5)
In this cha-pter it is assumed -1-hat the el.ec.trica1 conductivity o is
a fun~tion of depth z (positive downwa~ds) on1.y. In this case -the
electromagnetic field inside and outside the conductor can be re-
presented in terix of two scalars and $N(~) denoting the elec-
L -
tric and magr,e"ric. type of solution. These fields are defined as
'% .
follows IS the vector in z-direc-tion):
h A
On using t11.e. ident::.t)i- curlC$z) - = '-z - x gl~adC, Cfrom (2. 4 ) 1, i-t is se@!
.that -the ?$-type solu.!:ion has no nagne-tic z.-component and .the E-type
solution has no electrical .- z-component.