The force between two wires

Two parallel current-carrying wires will exert forces on one another.

Let's say wire 1 carries a current I1 out of the page. Wire 2, a distance d from wire 1, carries a current I2 out of the page. Assume that both wires are long. How much force does wire 1 exert on wire 2? What direction is the force?

The direction of the force experienced by wire 2 is:

  1. left
  2. right
  3. up
  4. down

Using the infinite wire equation, wire 1 sets up a magnetic field that wire 2 experiences. The magnitude of this field, at wire 2's location, is:

B1 = mo I1 / 2pd directed up.

To find the force on wire 2, use:

F = I2L ´ B1

We don't have a length to use for wire 2, but at least we can get the force per unit length:

F/L = I2 B1 = mo I1 I2 / 2pd

By the right-hand rule, a current out of the page in a field up gives a force to the left. Two parallel wires carrying currents in the same direction attract one another; wires with currents going in opposite directions repel.