The field picture of the interaction of two electric charges is that each charge produces an electric field that pushes or pulls on the other charge. We have a similar picture of the interaction between two currents: the current in each wire produces a magnetic field that pushes or pulls on the other current. If two neighboring wires carry currents in the same direction, they attract each other, while if they carry currents in opposite directions, they repel each other. For example, the two wires in the power cord of a table lamp exert magnetic forces on each other, and since the AC current oscillates, the forces oscillate. These oscillating forces are the source of the hum that you hear in many electrical appliances. If you need to find the magnitude of the force between two long parallel wires, simply compute the magnetic field produced by one wire at the location of the other, then use F = I L B from Chapter 29 to get the force.
Current-carrying loops also exert forces on each other, and it is easy to find the directions of these forces if we use the idea of the dipole moment to convert the loops into magnets. Once the right-hand rule has been used to find the directions of the dipole moments of each loop, just think of the loops as magnets; usually this makes it possible to decide whether the loops attract, repel, or twist each other. Just remember that the dipole moment vector of a magnet points from its south pole to its north pole when converting loops into equivalent magnets.