problem on finding maximum torque on a simple loop

[patlai]

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 ive tried everything and i can't seem to figure this problem out.

[patlai]

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.

[Tide]

I think you would maximize the area by bending the wire into a circular shape.

[Spectre5]

how did you get that answer patlai?