Maximum torque on an electric motor

[Dione]

Homework Statement

In an electric motor, a coil with 200 turns of radius 2 cm can rotate between the poles of a magnet. The magnetic field strength is 0.2 T. When the current through the coil is 50 mA, what is the magnitude of the maximum torque that the motor can deliver?

Variables
N = 200 turns
R = 2e^-2 m
B = 0.2 T
I = 50e^-3 A

τ = ?

Homework Equations

F = ILB
B = µ₀(N/L)I/sqrt (1 + (2R/L)²)

µ₀ = 1.257e^-6 N*s²/C²

The Attempt at a Solution

I first wanted to find what the L was so I could solve for the force. So I tried that. That didn't work out too well. I then tried anything. I'm still not sure I entirely understand the concept. I cannot receive credit for the problem even if I get it right anymore, but I'd like to know how to handle this if it pops up on the exam.

http://img48.imageshack.us/img48/1562/electricmotor1oc1.th.jpg

Thanks for any and all help,
Dione

 

[marcusl]

The torque arises ultimately from the Lorentz forces on the charges moving at velocity v within the wires
$$\vec{F}=q\vec{v}\times\vec{B}$$.

Look in your text, or in a book like Reitz and Milford, Foundations of Electromagnetic Theory. You'll see that, for a loop or coil, the torque T becomes proportional to coil current I and area A
$$\vec{T}=I\vec{A}\times\vec{B}$$.
$$I \vec{A}$$ is defined to be the magnetic moment.