Scaling question

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Question for David and group:

I've modelled a simple C core type electromagnet with two sets of
coils in femm based on a design we are considering building. We are
looking at building a quarter scale prototype first to make sure we
can produce the fields the numerical solution tells us we can. I've
noticed however, that in scaling down the original design by 1/4 and
recalculating in femm, much smaller fields are produced in the
airgap. Only by multiplying the original current density by 4 are the
original fields of the full scale model produced along the centerline
of the airgap. I had assumed that I would want to keep the current
density fixed while scaling the model down; the numerics seem to be
saying this is wrong. Can anyone explain why this is so?