130911-1106 EDT
Electric Sam:
Take a length of wire and form this into a tightly packed hairpin shape. Run a DC or AC current thru the wire. The current flowing toward the closed end is exactly opposite in direction to the current flowing from the closed end, and of equal magnitude. A short distance sideways from this loop these two fields essentially cancel one another.
Next expand the hairpin shape into a circular path. At the center of the circle the fields add, and at any point within the circular path. Go outside the current path and the fields start to cancel. Go sufficiently far away and there is almost complete cancellation.
An informative problem would be to write an equation for the magnetic field intensity as a function of the radial distance from the center of the circle. This might be in radial units normalized to the circle radius. Easier, if you make it an infinitely long rectangle. You can also do this experimentally with an N turn loop R1 in radius, possibly a 1000 turn sensing coil, and using AC excitation.
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