Problem # 1 (15 points): An eight-turn coil encloses an elliptical area having a

Question

Problem # 1 (15 points): An eight-turn coil encloses an elliptical area having a major axis of 40.0 cm and a minor axis of 30.0 cm. The coil lies in the plane of the page and has a 6.00-A current flowing clockwise around it. If the coil is in a uniform magnetic field of 2.00 x 104 T directed B toward the left of the page, what is the torque produced on the coil? In which direction will it rotate? Hint: The area of an ellipse is A = ab, where a and b are, respectively. the semimajor and semiminor axes of the ellipse. 40.0 cm 30.0 cm-

Explanation / Answer

The torque on any shaped plane current loop with current "i", area "A" and "N" turns is;

T = N(iA) X B

The direction of the first vector is perpendicular to the plane of the loop found by curling fingers of right hand around the perimeter in the direction of "i". Your thumb points in the direction of vector "iA" (also called the magnetic moment "u".
In your case "B" is perpendicular to vector (iA) and the magnitude of the torque is simply;

T = NiAB
= Ni(pi)abB , a&b are semi major/minor axis of the ellipse.
= (8)(6)(pi)(.4/2)(.3/2)(2x10^-4)
= 9 x 10^-4 N-m

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