# Force between perpendicular wires in the same plane

## Homework Statement

I was just wondering, so lets say there are two current carrying wires in the same plane that are perpendicular. One of them is infinite length, the other is a wire segment some distance away from the first one and perpendicular to it. What's the force on the wire segment?

## The Attempt at a Solution

People have been saying it's zero cuz the magnetic field is parallel to the wire segment, but I don't think that's true. I think that it's still perpendicular so there'll be a force on it. Am I right?

mfb
Mentor
How can a finite wire have a current inside?
The magnetic field would be perpendicular to the wire (and perpendicular to the whole plane of the setup).

I meant to say, wire segment part of a (probably) infinite wire. Sorry. In that case, would there be a force?

mfb
Mentor
This might get interesting at the intersection.
Well, apart from that: Sure, current and field are perpendicular to each other.

Hmmm... I don't see how the current and magnetic fields would be perpendicular... sorry I'm so dumb T_T but in the [very crudely drawn] diagram, imagine the current in the vertical wire is going upward. So that means, the magnetic field would be going into the page to the right of the wire. The other wire, which is also in this plane, has current flowing either left or right, it doesn't matter, but isn't the magnetic field from the first wire (into the page) perpendicular to the current in the second wire (planar with page)?

#### Attachments

• wire figure.png
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mfb
Mentor
So that means, the magnetic field would be going into the page to the right of the wire. The other wire, which is also in this plane, has current flowing either left or right, it doesn't matter, but isn't the magnetic field from the first wire (into the page) perpendicular to the current in the second wire (planar with page)?
Correct. Why don't you understand your own explanation?
I don't see how the current and magnetic fields would be perpendicular

OK, so there WOULD be a force on the horizontal wire, right?

mfb
Mentor
Of course.

OK, thanks for clearing things up :)