Square vs rectangular coil torque ratio with same wire length

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NotaPhysicsMan
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Hey,
Any help will do:

A square coil and a raectangular coil are each made from the same length of wire. Each contains a single turn. The long sides of the rectangle are twice as long as the short sides. Find the ratio t(tau) square/t rectangle of the maximum torques that these coils experience in the same magnetic field when they contain the same current.

Ok what I know:

t=Fl, maximum torque is when the normal is at 90 degrees to the field.
I know that the lengths for all sides of the square are equal, so x.
And the rectangle has two sides x, and two sides 2x. Since we want max torque, we want the bigger lever arm so I'll use 2x.


----o---- 2x rectangle
--o-- x square

Ok so t=Fl
=IABsin@/IABsin@
=I(x^2)Bsin@/I(2x(x)Bsin@)
Since the I, B and sin@ are constant

ts/tr= x^2/2x^2
ts/tr=1/2? :confused:

Anyone want to verify thanks!
 

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Aren't these two statements contradictory?

NotaPhysicsMan said:
A square coil and a raectangular coil are each made from the same length of wire.

NotaPhysicsMan said:
I know that the lengths for all sides of the square are equal, so x.
And the rectangle has two sides x, and two sides 2x.

Your rectangle is using 1.5 times as much wire as the square.
 
OH crap, I see. Ugh well let's see then 1.5 x for each side of the square.

Therefore ts/tr= (1.5^2)/(2)=1.125
!
Thanks for the reminder!