Perpendicular wires carrying current, torque

[caimzzz]

Homework Statement

Two thin wires of length $$L_1, L_2$$ were placed perpendicular to each other in half of their lengths. Wires are carrying current $$I_1$$ and $$I_2.$$ Find the torque on each of those wires.

Homework Equations

$$\tau = \mu \times B = r \times F$$

The Attempt at a Solution

To calculate the force I need the magnetic field, which I don't really know how to calculate in this problem. Calculating the magnetic dipole moment would require surface area, which I guess is zero(wires are infinitely thin) so it's a dead end. In parallel lines problem I could calculate magnetic field and force easily in any point in space, but I guess I can't really do that here because there is no distance between the wires. Where should I start?

 

[BvU]

Hello zzz and welcome to PF.

Re distance:
The thing to do is not to let that lack of info stop you: call this distance d, or use 1 m to begin with, whatever. Perhaps it cancels later on...

Re μ: doesn't appear , so I don't know what it stands for here ;)

Re: magnetic field: you should be able to find something on the magnetic field due to a current carrying wire...(If you can for parallel wires, you can also do it for perpendicular ones: B fields simply add up -- and wire 2 only "feels" the field from 1 anyway)

(By the same token as the distance: B field of infinitley long wire to begin with: what changes (strength, direction) if length is finite...)