# How does balancing currents within a cable or conduit cancel its magnetic fields?

I know the NEC requires all current carrying conductors of the same circuit to be included in the same cable or conduit [300.3(B)], but why? I think it is because the magnetic field generated by current within a single conductor would cause inductive heating in nearby metals, and if the other circuit conductors were included their magnetic fields would cancel each other out. But I don't understand how that works.

I watched several YouTube videos showing the magnetic fields around magnets and single conductors, but no one really explained how two sides of the same circuit, with one current traveling in one direction and the other equal current returning in the other direction, cancel each other's magnetic field. In one video, two magnets faced one another with their north poles forced together; it effected a reduction in the magnetic field. If one magnet was flipped, they attracted and this increased the magnetic field.

So, in a cable with the directions of current opposing one another, it seems to me this would also cause these to be opposite forces, thus attracting one another and making the magnetic field stronger. I guess I just don't understand the rules very well. Can someone explain?

• Are you familiar with Maxwell's equations? Commented May 4, 2022 at 2:22
• Make a thumbs up with your right hand. Your thumb points in the direciton of current in the wire. Your fingers are the magnetic field lines circulating around the wire as a result of the current. Now make a thumbs down for the current in the opposite direction. notice how your fingers point in opposite directions and cancel out the magnetic field from the current that is going up? Of course, magnetic fields an intensity and direction and those intensities must be equal to actually cancel out as much ass possible and that is only true if the currents going in opposite directions are the same. Commented May 4, 2022 at 2:59
• By the way, the wrong way to start understanding magnetic fields is to try and figure out how a permanent magnet field interacts with the magnetic field generated by current in a straight wire since as you've found, it's not as straightforward as it might seem since permanent magnets have a clear north and south pole, and so does wire wound up into a coil, but a straight wire not so much. Commented May 4, 2022 at 3:07

To start, currents are not the same as bar magnets (i.e. permanent magnetic dipoles).

Consider a pair of conductors carrying equal-but-opposite conventional currents (red):

By the right hand rule, we can draw the magnetic field (blue) associated with each of them:

Note that these two magnetic fields curve in opposite directions around the wires. For the right conductor, it curves clockwise in our field of view. For the left conductor, it curves counterclockwise in our field of view. These extend further out, but drawing the overlap would lead to a messy image.

The magnetic fields created by two conductors can be combined with superposition. The validity of superposition follows from the linearity of the integral in the Biot-Savart law.

Note that above the wires, the field cancels (but it is too messy to easily draw): the left wire provides a magnetic field pointing left, while the right wire provides a magnetic field pointing right. Below the wires, same cancellation: left wire provides field pointing right, right wire provides field pointing left. Far to the left, the left wire provides field pointing down while the right wire provides field pointing up.

The fields only add together to make a stronger field in the middle, right between the two wires. This only has a significant effect very close to the cable, and does not lead to a substantial magnetic field outside of the cable/conduit. The net field looks like this:

with negligible field away from the wires.