Ampere's Law

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.

  1. Loop 3 > Loop 1 > Loop 2
  2. Loop 3 = Loop 1 > Loop 2
  3. Loop 3 > Loop 2 > Loop 1
  4. Loop 2 > Loop 3 > Loop 1
  5. none of the above

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