An eight-turn coil encloses an elliptical area having a major axis of 40.0 cm an

Question

An eight-turn coil encloses an elliptical area having a major axis of 40.0 cm and a minor axis of 30.0 cm (see figure). The coil lies in the plane of the page and carries a clockwise current of 6.07 A. If the coil is in a uniform magnetic field of 1.99 X 10-4 T directed toward the left of the page, what is the magnitude of the torque on the coil? Hint: The area of an ellipse is A = pi ab, where a and b are, respectively, the semimajor and semiminor axes of the ellipse. The torque that a uniform magnetic field exerts on a flat (planar) coil is given by tau = NBIAsin theta, where N is the number of turns of wire in the coil, B the magnitude of the magnetic field, I the current flowing in the coil, A the area enclosed by the coil, and theta the angle between the line perpendicular to the plane of the coil and the direction of the magnetic field. The expression given above was derived for a rectangular coil but it is valid for any planar coil. The area enclosed by the coil can be square, rectangular, circular, ellipsoidal (as in this problem), or any other two-dimensional shape. In the situation shown in the figure redrawn below, the magnetic field is parallel to the plane of the coil. Thus, the angle between the magnetic field and the line perpendicular to the plane of the coil is theta = 90.0degree. With a semimajor axis of a = (0.400 m)/2 and a semiminor axis of b = (0.300 m)/2, the area enclosed by the coil is A = .pi ab =.03 pi m2, and the magnitude of the torque exerted on the coil is tau = NBIAsin theta = 8( x 10-14 T)( A)( pi m2) sin 90.0degree = x 10-14 N m. Note that by the right-hand rule, the magnetic force exerted on the left side of the coil is directed out of the page while the force exerted on the right side is into the page. Thus, an observer looking from c toward d along the dashed line shown in the diagram sees the coil rotate counterclockwise.

Explanation / Answer

I am meant to be using the force acting on the current carrying wire. I thought I could just use the t = ucrossB forumla in the form: t = ubsintheta where u = IA

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