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

In summary: This forces the current to flow in a circle around the loop.In summary, the current in the loop is 4.4e-8 N·m.
  • #1
RKOwens4
33
0

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.)
 
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  • #2
RKOwens4 said:
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.
 
  • #3
lewando said:
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)?
 
  • #4
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
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
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.
 

1. How do you calculate the current in a loop when torque and magnetic field are given?

To calculate the current in a loop, you can use the formula I = T/BA, where I is the current, T is the torque, B is the magnetic field, and A is the area of the loop.

2. What are the units of measurement for torque and magnetic field?

The units of measurement for torque are Newton-meters (N·m) and the units for magnetic field are Tesla (T).

3. Can you calculate the current in a loop without knowing the torque or magnetic field?

No, both torque and magnetic field are necessary in order to calculate the current in a loop. Without these values, the current cannot be determined.

4. How does the direction of the magnetic field affect the current in a loop?

The direction of the magnetic field does not affect the magnitude of the current in a loop, but it does determine the direction of the current. The current will flow in a direction perpendicular to both the magnetic field and the direction of the torque.

5. What is the significance of calculating current in a loop?

Calculating the current in a loop is important in understanding the behavior of electric circuits and electromagnetic systems. It helps determine the strength and direction of the current, which can be used to predict the effects of the magnetic field on the loop and vice versa.

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