We investigate how different magnetization distributions interact with
an external electromagnetic field. Strong selectivity to the time dep
endence of the external electromagnetic field arises for particular ma
gnetizations and suggests that it can be used for practical applicatio
ns. We review the properties of the known charge-current radiationless
configurations. The radiation field of toroidal-like time-dependent c
urrent configurations is investigated. Infinitesimal time-dependent co
nfigurations are found outside which the electromagnetic field strengt
hs disappear but the potentials survive. For a number of time dependen
ces, their finite radiationless counterparts can be found. In these ca
ses topologically nontrivial (unremovable by a gauge transformation) e
lectromagnetic potentials exist outside the sources. The well-defined
rule obtained for constructing time-dependent infinitesimal sources su
ggests the existence of finite nontrivial radiationless sources with a
rather arbitrary time dependence. The latter can be used to carry out
time-dependent Aharonov-Bohm-like experiments. Examples are given of
nonstatic current configurations generating the static electric field
and adequately described by the electric vector potential rather than
by the scalar one. (C) 1998 American Institute of Physics.