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 coll lies in the plane of the page and has a 5.77-A current flowing clockwise around it. If the coil is in a uniform magnetic field of 1.91 x 10" 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 - nab, where a and bare, respectively, the semimajor and semiminor axes of the ellipse. 40.0 cm |-30.0 cm Step 1 The magnitude of the torque that a uniform magnetic field exerts on a llat (planar) coil is given by T = x B - NIAB sin , where N is the number of turns of wire in the coll, I the current in the coil, A the area enclosed by the coil, B the magnitude of the magnetic field, and 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 in the textbook 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. 40.0 cm

Answer 1

major axis axis 30cm 2 Y,umber of turns, n=8 length zºom minor Current in clock wise coreation magnetic field, B = angle 5.77 1.91x50T between magnetic field and magnetica moment, o =90o. TE ma 13: I. se 7B 0.3 Area of an ellip = Tas = 3.148 0 4 X 0. 013768 20:0948 2 m m- DIA 4.348 Ang2 8 x 5.77 0.3768 s ms Torque, a MB sin goo 4.34881.grxio 8.3x104 Mom