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electric filed intensity visualization



I've noticed a lot of thread topics here besides pure FEA, so I would
like to ask a fairly abstract question to the group, getting right
back to Maxwell's equations. I would really like to be able to
visualize the magnetic circuit properties just like an electric or
fluid circuit, but I am having trouble with the H.

While I have been working with solenoids and electrical machines for
years, I just realized I have trouble visualizing what the meaning of
amps/meter is. I never really thought about this until a was working
with a permanent magnet in FEMM, and even though there is no electric
current, there is still a lot of H. How does one sense the field
directly, without depending on the resulting magnetic flux? If all of
those coulombs are crossing a boundary, where is the boundary and
where are they going?

Any enlightenment would be appreciated. Thanks.