Problem on finding maximum torque on a simple loop

AI Thread Summary
To find the maximum torque on a rectangular loop of wire in a magnetic field, the loop's dimensions must be optimized. The torque is influenced by the area of the loop and the magnetic field strength. A common approach is to consider reshaping the wire into a circular form to maximize the area, which can lead to increased torque. The initial calculation provided was B*I*((l+h)/2)^2, but it was noted that this answer is incorrect due to a missing multiplicative factor. The discussion emphasizes the importance of optimizing the loop's shape to achieve maximum torque in the magnetic field.
patlai
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The plane of a rectangular loop of wire with a width of W and a height of L is parallel to a magnetic field of magnitude B. The loop carries a current of I .

What is the maximum torque that can be obtained with the same total length of wire carrying the same current in this magnetic field?


*note i feel like I've tried everything and i can't seem to figure this problem out.
 
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i know you have to do something with optimizing the area

i got this answer:

B*I*((l+h)/2)^2

but the website system says my answer is off by a multiplicative factor.
 
I think you would maximize the area by bending the wire into a circular shape.
 
how did you get that answer patlai?
 

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