Imagine a square current-carrying superconducting loop with one side of the
four (say, the bottom side) coated with a magnetic material of high relative
permeability. The axial vector lies parallel to an omnipresent external
magnetic field (Earth's for example), so there is zero restoring torque (it is
not of interest anyway). To my naive estimation, there now exists a
unidirectional force on the coil.
The force felt by any side of the loop is B*I*L = u*H*I*L, where
H = earth's H-field
u = permeability
I = loop current
L = length of a side of the square loop
So the left side feels a force leftward F_l
So the right side feels a force rightward F_r
So the top side feels a force upward F_u
So the bottom side feels a force downward F_d.
F_l = F_r
F_u =/= F_d
It flies. If not, why not?
-Andrew
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