Magnitude of torque in a circuit?

[Violagirl]

Homework Statement

What is the torque in the circuit in the attached document?

Homework Equations

τ = μ x B

μ = (I)(A)

The Attempt at a Solution

See attached document for solution. I'm very confused by how to relate each torque together. I know that for each segment of wire, that there will be different torques and the total amount of torque in the circuit can be summed by the amount of torque in each segment of wire. I have one segment pointing in a downwards y direction, another that points in the -x direction, and the last that is perpendicular, so it is a triangular shaped current. For the perpendicular segment, I know that it can will have torques at the x and y-axis using sin and cosine of the angle formed. However, I'm not sure I recall how to sum torques in different directions or how to properly relate them together? Any help is appreciated.

 

[Basic_Physics]

The direction of the magnetic dipole moment $\vec{\mu}$ is determined by using the right-hand rule. Curl the fingers in the direction of the current around the loop. The thumb points in the direction of $\vec{\mu}$. The torque on the loop, $\vec{\tau}$, is then determined by the vector product

$\vec{\tau}=\vec{\mu}\times\vec{B}$