This question comes from a thought I had in my physics lecture today.

Lets say you have two of the same size conductors with two equal currents running through them in the same direction.

Both of these currents would produce a magnetic field. Between the two conductors, the direction of the magnetic fields would be opposing each other. So between the two conductors, the superpositions of the magnetic fields should cancel each other out.

 

Yet, in lecture, my professor said that there is still an attractive force between these two conductors. But, isn't the force dependent on the magnetic fields? Why is there still this force, when the magnetic fields should cancel each other out (at least in the middle)?

If the current in both conductors has the same direction, then there is attractive force between them, is the direction is opposite then there is repulsion between them. From Amperes force you can derive the force acting between the conductors which is [math]2\times 10^{-7}N[/math]

 

Cancel each other out? They're not in direct contact with each other, only close to!

The force is due to the field where the wire is, not at some other point.

The force is due to the field where the wire is, not at some other point.

 

But the magnetic field would be created outside the conductor, as all the charges in the conductor would flow at the edges.

But the magnetic field would be created outside the conductor, as all the charges in the conductor would flow at the edges.

Does this make any difference?

Still, the force on wire A is due to the field emanating from wire B, present at wire A. Not at some point halfway in between, where the fields cancel.

 

In reality, it would be due to the fields throughout the wire, which will have thickness and thus see a field gradient, and also depend on the current density distribution, but it's reasonably represented by an infinitely thin wire and the field at a point.