Schmucker-Weidelt Lecture Notes, Aarhus, 1975 - MTNet

All field quanti-ties are functions of position _r and time t. Al.so tl:c
(isotropic) conductivi.-t)~ u is a func.tion of position. -e I 3,s the
current density of the external cilrrent sources being different from
0 only at source points. The displacement current c 0- E is generally
neglected in induction studies. This is justified as follows: within
the conductor -- .the conduc-tion current UC - exceeds the displ.acement
current even in the case of ].owest periods (0.001 sec) and highest
5 2
resis1:ivities (10 Rm) still 10 times. In the vacuum where .the
conduction current is absent the inclusion of the, displacsment
current merely introduces a slight phase shift of the external field
at different points. for in this case the solution of (1.2) and (1.3
(including at the RFIS of (1.2) ) are electromagnetic waves, e. g.
the plane wave e i(k*r - - - u ~ ) where , w is the angular frequency and
.- k the wave vector along the direction of propagation. The phase
difference
4
between P and P2 is
1
,/ case
- .
PI Ax P2
MAX
l,j&t = -- coscl
C
.Z in the very pessimistic
of Ax = 1000 km and T = lse
- H ar~d - .I can he eliminated fPonl (1.. 2 - (1.4). It results
L Induction equation
----- - I
6!t using C1.2) and (1.4) the elec-trical charge density p(1') - is
given by
p = E div - E = - c E - grad I.oga, (1.7)
0 0 -
i.e. there is charge accumulated if an electrical field compunclnt :
parallel to the gradj.en.t. of the conductivi-ky. Physically 'this is
cl.ear,, since the normal. componen-t of .the current density is conti-
nuous whereas the charges accoun-i: for tl-~e corresponding discon-ti-
nuity of the normal electri.cal. field.