This Demonstration computes the magnetic field produced by a pair of square Helmholtz coils. The results are much more straightforward than those for the more conventional circular Helmholtz coils, which involve elliptic integrals. You can adjust the field at the center of the coils so that over a small region of space it cancels the Earth’s magnetic field (which ranges from about 0.3 gauss to 0.6 gauss).