2.3.4 Low-Frequency Breakdown
In general, the electric field due to an arbitrary electric current 
involves two parts, namely, the vector-potential part
and the scalar-potential part
where 
. As the frequency decreases, the scalar-potential part dominates the vector-potential part. In fact, using finite-precision arithmetics, the vector-potential part can be lost during numerical solutions. On the other hand, (2.235) is not a one-to-one map between the electric current and electric field. Specifically, for a given 
, there are infinitely many 
. This is because, for a nonzero frequency, 
may have a solenoidal part 
such that
and this solenoidal part contributes to the electric ...
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