Comparing maximum torques of square and rectangular coils

[vaxopy]

A square coil and a rectangular 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 tsquare/trectangle of the maximum torques that these coils experience in the same magnetic field when they contain the same current.

Im very confused how to do this :/

 

[asrodan]

Let L be length of the squares sides. Using the fact that the perimeter's are equal you can write the length and width of the rectangle in terms of L.

Remember that torque = u X B where u is the magnetic dipole moment of the loop. Since there is no requirement for the magnitude or direction of B, you can just let B=1 and be perpendicular to u so that u X B = u.

 

[michaelw]

i don't know if i did this right
it seems too easy..
t = torque, s=square, r=rectangle

t = NIABsino (o = theta)
ts/tr = NIAsB/NIArB = As/Ar = L^2/2L^2 = 1/2

is this right?

 

[asrodan]

Your right in that it's just the ratio of the areas, but you don't have the correct area for the rectangle. You know that 2 sides of the rectangle are twice as long as the other sides.

Use a different variable to define the sides of the rectangle then use the fact that the perimeters are the same to find the sides of the reactangle in terms of L.