Calculating current in a loop, given torque and magn. field

[RKOwens4]

Homework Statement

In the figure below, a rectangular loop carrying current lies in the plane of a uniform magnetic field of magnitude 0.038 T. The loop consists of a single turn of flexible conducting wire that is wrapped around a flexible mount such that the dimensions of the rectangle can be changed. (The total length of the wire is not changed.) As edge length x is varied from approximately zero to its maximum value of approximately 3.4 cm, the magnitude τ of the torque on the loop changes. The maximum value of τ is 4.4 x 10^-8 N·m. What is the current in the loop?

Figure: http://imageshack.us/photo/my-images/231/webassign.jpg/

Homework Equations

Torque(t)=NiABcos(theta) ------> i = t/(NABcos(theta))

The Attempt at a Solution

I tried solving it using the variation of the above equation, using 4.4e-8 for torque, 1 for N, 0.038 for B, and 0 for theta, but that leaves me without a number for area and the unused length value stated in the problem. If I use the equation i = F/(LB), that leaves an unknown value for Force. It seems like a simple plug and chug problem but I'm not sure what the equation to use is. (I'm also taking this as a summer course so my professor is forced to race through all of the material.)

 

[lewando]

As edge length x is varied from approximately zero to its maximum value of approximately 3.4 cm...

Does this not help you determine the loop perimeter? Assume full range of possible rectangle shapes is allowed by the flexible mount.

 

[RKOwens4]

Does this not help you determine the loop perimeter? Assume full range of possible rectangle shapes is allowed by the flexible mount.

It tells me that the length of the length of the wire (or, loop perimeter) is 6.8cm. I'm sure I could use that as a circumference to find the radius if it were a perfect circle (and hence, the area), but how do I know which shape to use? "Max value of torque" tells me that (if I'm supposed to be using the equation I stated in the opening post) that A should therefore be at a maximum. Hm, which produces the largest area: perfect square or perfect circle?

Also, am I working with the correct equation? And if so, what do I do about that cos(theta)?

 

[RKOwens4]

Ok, I just did a quick test and found that a perfect square gives the max area. But still, I'm not sure what to do with cos(theta).

 

[RKOwens4]

Well I finally figured it out! You just ignore cos(theta) so it becomes i=t/(NAB). Thanks for pointing me in the right direction.

 

[lewando]

Good work by you! Better to not ignore cos(theta), but to read "theta = 0", from the problem. The B field lines and a line normal to the plane of the loop are going in the same direction.