What is the magnetic field strength?

[IHave]

Homework Statement

A 14.2 cm - diameter circular loop of wire is placed with the plane of the loop parallel to the uniform magnetic field between the pole pieces of a large magnet. When 3.10 A flows in the coil, the torque on it is 0.135 m N. What is the magnetic field strength?

2. Homework Equations ;3. The Attempt at a Solution
Okay, I know that I need to find the value for B, the magnetic field; and that there are a number of equations that I can use. However, I am a bit confused, since torque is given; I know that it will be used in some way.

Any help is welcome!

 

[Delphi51]

That is a tough one! Unless you happen to have a formula for the torque on a circular coil in a magnetic field.

I can explain how to do it for a square coil, which should give you some understanding of your problem. A square coil will have four pieces of wire of length L, two of which are parallel to the B field and don't have a force on them. The formula for the force on the other two is F =I*L*B (see http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html#c2). This force F will be perpendicular to both the wire and the B field, and it will be in opposite directions on the two wires so they will try to rotate the loop of wire. The torque for this rotation will be F*L/2 for each of the forces because the force acts distance L/2 from the center of rotation.

If you happen to know calculus, you can think of your circular loop of wire as having an infinite number of segments, each of which has a component dL perpendicular to B. So you can figure out the torque for each of the segments and integrate to get the whole torque. Once you have the formula for Torque due to B, you can solve it for B to do your particular problem.