# Two current carrying wires (need clarification)

1. Jul 31, 2011

### physickkksss

1. The problem statement, all variables and given/known data

Two parallel wires carry current in same direction. Do they attract or repel each other?

2. Relevant equations

Magetic field (B) created around wire. Direction using Right Hand Rule.

F(mag) = I(L x B)

3. The attempt at a solution

When I work out the direction of F(mag) using the cross product rules, I can see that the force on each wire by the magetic field of the other wire is towards each other....therefore the wires attract.

But I dont get something:

The direction of B between the wires is actually against each other. One wire makes a field into the page, and the other out of the page. So shouldn't that make the magnetic fields repel each other?

Eg. When a north end of a maget approaches a north end of another magnet, the fields are in opposite direction, and they repel...

I know I got the direction of F(mag) right, so the wires are attracted. But something is just not clicking with the direction of B.

Thanks if anyone can clarify :)

2. Jul 31, 2011

### hubewa

If you drew a diagram of the two wires (carrying current in the same direction) interacting together, you would find that both fields join up and interact in a way similar to the north and south pole of a magnet. The field lines from one wire is joined to the field line of another.

If the current was in different directions, this would result in the field lines not joining up, similar to a North-north magnetic field, which repels.

This may not be correct but it could be a starting point.

I hope this has helped you "kind of understand it".

3. Jul 31, 2011

### physickkksss

Well, when I draw it out:

The F(mag) on the current in each wire, from the magnetic field of the othe wire, point towards each other. That is why I'd say the wires are attracting each other.

But, in between the wires, the magnetic fields actually go in opposite directions (one out the page, one into the page)...I want to know what does this mean. According to that, shouldnt the wires be pushing apart?

4. Jul 31, 2011

### PeterO

Your statement about the field between the wires may indeed be correct, but that is of little interest. The force is induced at each wire, where each wire carries a current in the magnetic field created by the other wire.
Those fields between the wires will tend to cancel each other out, so there is zero B along that line exactly in the middle.
If you got a third wire and placed it down the centre, there would be no net force on that wire. Of course you may be convinced that the left hand wire is attracting it left, while the right hand wire attracts it right and it is the Induced Forces that cancel, rather than there being no induced force at all -

5. Jul 31, 2011

### physickkksss

Ok so F(mag) pulls each wire together...I got that much

But if the magetic fields between the wires repel each other, won't that oppose the F(mag) force? Then maybe the wires come to some kind of equilibrium, where the pull force equals the opposing force?

I keep thinking of bringing two North ends of a magnet together. If the magnetic fields are in opposite directions, they push apart. So how is that different from the situation with two current carrying wires?

6. Aug 1, 2011

### PeterO

Neither of the two wires can ever be in the middle of the two wires?????

One of them may be where the middle used to be, but that will in fact result in an even large force, because it is now in a region of even stronger magnetic field from the other wire [assuming that other wire wasn't moved.