Ampere's Law allows us to easily calculate magnetic fields in highly symmetric situations, much as Gauss' Law allowed us to determine electric fields.
Ampere's Law states that the line integral of B · ds around a closed (i.e., complete) loop is proportional to the current passing through the loop:
Around a closed loop ò B · ds = mo Ienc
Question: Rank the three closed loops above according to the magnitude of the net current enclosed, from largest to smallest. Four current-carrying wires are present. The three in red carry currents of I, 2I, and 3I out of the page; the one in blue carries a current of 3I into the page.
The answer is that Loop 3 has 6I passing through it while Loop 1 and Loop 2 each have 3I (the 3I into the page cancels the 3I out of the page for Loop 2). So:
Loop 3 > Loop 1 = Loop 2