Two wires are laid out in the xy plane so that they are perpendicular and their
ID: 1793715 • Letter: T
Question
Two wires are laid out in the xy plane so that they are perpendicular and their centres of mass line up in the xy plane (they form a cross-like shape) Looking from above, each wire appears to bisect the other. One wire is infinitely long, the other has a length L 18.66 m. Both wires carry 3.02 kA of current and the wires are separated by a z distance of 1.22 m. Determine, in Nm, the magnitude of the torque on the small wire due to the magnetic interaction. Give your answer with 3 significant figures Selected Answer: Correct Answer: 34.11 27.6 ± 20%Explanation / Answer
wire length, l1 = inf
l2 = 18.66 m
i = 3.02 kA
z = 1.22 m
consider a small part dx of the finite wire at coordinate x
then
magnetic field due to infinite wire B = 2*ki/sqroot(z^2 + x^2), at angle theta with horizontal
tan(theta) = x/z
hence force on this small segment = dF = Bidl sin(theta) = 2*ki^2*xdx/(z^2 + x^2)
torque = dF*x = 2*ki^2*x^2dx/(z^2 + x^2)
net torque = integrate dT from x = -l2/2 to x = +l2/2
T = 2*k*i^2*dx - 2ki^2*z^2*dx/(z^2 + x^2)
T = 2ki^2(l2) - 2ki^2*arctan(l2/z)/z
T = 31.40859 Nm
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