# Attraction between two wires with parallel current

I'm self-studying electric and magnetic forces, and I'm stuck on one concept that I can't seem to resolve.

The book I'm using (College Physics Reasoning and Relationships, Giordano) explains a situation between two horizontal parallel wires. If a parallel current is run to the right in each wire, there will be a magnetic field encircling each wire. The top wire (in a diagram of the magnetic field) will have x's below the wire and dots above, but so will the bottom wire.

The book explains that ignoring the magnetic field of the lower wire, the magnetic force on the lower wire will be aimed toward toward the above wire, and vice versa. This makes sense to me if we ignore each magnetic field to see each magnetic force.

My confusion comes in that my initial reaction is that if the magnetic fields in between the two wires would be superimposed the result would be a zero magnetic field. I think I thought of this because the book explains that potential and electric fields could use the principle of superposition to figure out the strength at each point.

Can someone explain why there isn't a superposition of fields, or explain what's wrong with my thinking here?

Thanks!

• There should be a point exactly between the two wires (assuming they have equal current) where the magnetic fields cancel each other out entirely. Aug 12, 2016 at 15:39

Of course there is superposition. There will be cancelling out of fields in some places. If the currents are of equal magnitude, that 'null' point will lie somewhere midway between the wires. The more you increase the current in one, more will the 'null' point shift towards the other wire.

• This helps me because I now realize after a bit more digging that the strength of the magnetic field is inversely related to the radius from the wire. The problem I still see is that under superposition the field closer to the upper wire would overwhelm the field coming from the lower wire, and so the magnetic force would not be present if we focus on the point on the upper wire. I'm trying to be clear, but if I picture the magnetic fields separately, it makes sense. But if I superimpose the magnetic field first, I have trouble finding the same magnetic forces.
– Jim
Aug 12, 2016 at 15:56
• This is very much like gravity. I'm sure you must have done the grade school problems like 'there is a mass A and mass B separated by a distance R, where should another mass C be kept so that it feels no force'. Same here. Where should a compass be kept to show no deflection? is the question in this case. Aug 12, 2016 at 16:00
• This makes sense. To make sure I understand this, does this mean that in the idea of superposition each individual field is independently existing, but mathematically we can find the "effect" of all the fields together at one point? Or does superposition mean that we can ignore all original fields if we simplify them down into one field?
– Jim
Aug 12, 2016 at 16:11
• @Jim I'm not quite sure what you are trying to describe. Perhaps the problem is this: there is no force on a wire due to the field that it itself produces. Aug 12, 2016 at 16:21
• @garyp I think you hit it on the head and that resolves my initial misconception.
– Jim
Aug 12, 2016 at 16:32