Helmholtz coils can be used to cancel the Earth's magnetic field over a region of space by generating a uniform magnetic field of equal magnitude but opposite direction. For square coils, the easiest way to calculate the magnetic field
is first to calculate the vector potential
due to each coil and then to take the curl of
in Cartesian coordinates. The region over which the field is uniform is determined from the plots of
versus
and
versus
. The magnetic field lines in the
plane are given by the contours of the scalar function
, since
.
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