Question

5. A square coil and a rectangular coil are each made from the same length of wire. Each contains a single turn. The long side of the rectangle is 2.4 times the short side. Find the ratio (squareTrectangle) of the maximum torques that these coils experience in the same magnetic field when they contain the same current.

Answer 1

5. given a square coil, rectangular coil

same length of wire

n = 1

for rectangel

width = w

l = 2.4w

so the ratio of maximum torque will be ratio of the areas

hence

Ts/Tr = As/Ar

As = a^2

Ar = lw = 2.4w^2

now, 4a = L

2l + 2w = 6.8w = L

hence

Ts/Tr = L^2*(6.8^2)/16 * 2.4*L^2 = 1.2041666