A current loop near a long straight wire

We stated previously that a current loop in a uniform field will experience no net force. What about a current loop near a long straight wire? Consider the situation shown above, where a loop with a clockwise current I2 is placed near a long straight wire carrying current I1 to the right. In this case the net force on the loop is:

  1. left
  2. right
  3. up
  4. down
  5. into the page

To answer the question, consider the force experienced by each of the four sides of the loop. Let's say the loop has a width a, and height b, and the distance between the loop and the wire is d.

The force experienced by the top side of the loop is directed up:

F1 = mo I1 I2a / 2pd

The force experienced by the bottom side of the loop is directed down:

F3 = mo I1 I2a / 2p(d+b)

This gives a net force up, toward the long straight wire.

The forces on the left and right sides are difficult to calculate, but they cancel one another so we don't need to worry about them.