Since magnetic forces can do no work, what force IS doing the work when a bar magnet causes a paper clip to jump off a table and stick to the magnet?
Asked by: Steven Leduc
The original assumption that a magnetic field can
do no work is incorrect. A magnetic field has
an energy density that is equal to the magnetic
induction (B) squared divided by twice the
permeability (mu sub zero). If you were to sum
(integrate) this energy of the magnet over all of
its field before it picked up the paper clip and
compared it to the same sum after you picked up
the paper clip, you would discover that there was
a loss of field energy. The paper clip has in
effect 'shorted out some lines of magnetic flux'.
How much energy was lost? If you took hold of
the paper clip and pulled it out to such a
distance that the magnetic pull was insignificant,
the work you did in this process would exactly
equal the amount of energy lost when the clip was
on the face of the magnet. When you picked up
the clip with the magnet the clip was accelerated
toward the magnet acquiring kinetic energy. This
kinetic energy will equal, ignoring air drag,
the loss of magnetic energy in the field.
This kinetic energy will be dissipated in the
form of heat on impact of the clip with the
For further understanding of the energy
in a magnetic field, you may want to study
magnetic fields in solenoids. See the Reference
Physics, Volume 2 by Halliday and Resnick
Answered by: Robert Gardner, M.S., Retired Physicist
'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'