# Homework Help: Calculating current in a loop, given torque and magn. field

1. Jul 3, 2011

### RKOwens4

1. The problem statement, all variables and given/known data

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/

2. Relevant equations

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

3. 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.)

2. Jul 3, 2011

### lewando

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

3. Jul 3, 2011

### RKOwens4

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)?

4. Jul 3, 2011

### 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).

5. Jul 3, 2011

### 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.

6. Jul 3, 2011

### 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.

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