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For a LVD (linear vector dipole) type source that is prolate in the
direction of the forces, most of the moment is required to deform
the outer medium, and only a small fraction remains to
expand the source itself. The medium counteracts the lengthwise
expansion of a thin and long body very strongly. The ratio between
the moment and the volume change of the source can be arbitrarily
large, as is apparent from the following model:
Two colinear forces of opposite direction act at some finite
distance *d* from each other. To avoid singularities of the
displacement field, we distribute each force over a small sphere
with a radius .
The source volume is defined as comprising
the two spheres and a narrow tube connecting them. Obviously,
the volume change within the source can be made arbitrarily small.
Most of the volume change occurs outside the source. Thus,
the ratio of moment to source-volume change can be arbitrarily large.

*Erhard Wielandt *

2003-05-30