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 to the right of wire 1, carries a current I2 out of the page. Assume that both wires are long.

Let's assume that I1 is a lot larger than I2. Which wire exerts more force on the other?

  1. Wire 1 exerts more force on wire 2 than wire 2 exerts on wire 1
  2. Wire 2 exerts more force on wire 1 than wire 1 exerts on wire 2
  3. Wire 1 exerts the same magnitude force on wire 2 as wire 2 exerts on wire 1

Newton's third law still works here, so the forces have the same magnitude.

If the two wires carry currents in the same direction, what is the direction of the force that wire 1 exerts on wire 2?

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

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 =
μo I1

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:
= I2 B1 =
μo I1 I2
2π d

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.