Two current elements are perpendicular to each other. Wire 1 is oriented vertically,has a current I1 flowing in the +Y direction, and has a length L1. Wire 2 is situated above wire 1, has a current I2 flowing in the -X direction, and has a length L2. Do the current elements I1L1 and I2L2 produce a force on each other? If so, what is the magnitude and direction of each? Do they violate newton's 3rd law? Below is my best reconstruction of the diagram my professor drew on the board today. Its kind of hard to draw this way but the only thing wrong with my diagram is that wire 1 should be centered with wire 2(not intersecting!)
The Attempt at a Solution
Beginning the first part of the problem, I tried to find the forces that the wires produced on each other. I believe that the Force on wire 1 due to wire 2(F12)=I1L1*B2. Using the right hand rule the B field caused by wire 2 is coming out of the page, below itself, and into the page above.
Now when it comes to the force on wire 2 due to wire 1(F21), I know the equation for F21=I2L2B1. The B field produced by wire 1 is out of the page to the left of wire 1, and into the page to the right.
Now that I have the magnitude of the Forces the wires produce on each other, and the direction of their respective magnetic fields, I believe my next step is to find the direction of the forces. Using the right hand rule for F12, I point my fingers in the direction of I1L1 and sweep them towards B2. This gives a direction of F12 in the +X direction.
Now for the direction of F21 I point my fingers in the direction of I2L2 and sweep them towards B1, but I don't know which direction this is since I can't decide how B1 interacts with wire 2. Does B1 interact with wire 2 at all? I'm stuck here and don't know if what I've done so far is even right.