The torque that a uniform magnetic field exerts on a flat (planar) coil is given byT = NBIAsin 0,where N is the number of turns of wire in the coil, B the magnitude of the magnetic field, I the current flowingin the coil, A the area enclosed by the coil, and 0 the angle between the line perpendicular to the plane of thecoil and the direction of the magnetic field. The expression given above was derived for a rectangular coil butit is valid for any planar coil. The area enclosed by the coil can be square, rectangular, circular, ellipsoidal (asin 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 cmB|-30.0 cm→|dThus, the angle between the magnetic field and the line perpendicular to the plane of the coil is 0 = 90.0°.With a semimajor axis of a =coil is(0.400 m)/2 and a semiminor axis of b = (0.300 m)/2, the area enclosed by theA = nab =Tt m2,and the magnitude of the torque exerted on the coil isT = NBIAsin 0| × 10-4 T)( [m2 )sin 90.0°= 8x 10-4 N ·m.Note that by the right-hand rule, the magnetic force exerted on the left side of the coil is directed out of thepage while the force exerted on the right side is into the page. Thus, an observer looking from c toward dalong the dashed line shown in the diagram sees the coil rotate counterclockwise. Tutorial ExerciseAn eight-turn coil encloses an elliptical area having a major axis of 40.0 cm and a minor axis of 30.0 cm (seefigure). The coil lies in the plane of the page and carries a clockwise current of 6.17 A. If the coil is in auniform magnetic field of 1.92 x 10-4 T directed toward the left of the page, what is the magnitude of thetorque on the coil? Hint: The area of an ellipse is A = nab, where a and b are, respectively, the semimajor andsemiminor axes of the ellipse.B40.0 cm- 30.0 cm-|

1. Area(A) 2. The magnitude of the torque. given, magnetic fieldB=1.92×10-4 TCurrentI=6.17 Asemi…

The torque that a uniform magnetic field exerts on a flat (planar) coil is given by T = NBIAsin 0, where N is the number of turns of wire in the coil, B the magnitude of the magnetic field, I the current flowir in the coil, A the area enclosed by the coil, and 0 the angle between the line perpendicular to the plane of th coil and the direction of the magnetic field. The expression given above was derived for a rectangular coil bu 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 В |-30.0 cm-| d Thus, the angle between the magnetic field and the line perpendicular to the plane of the coil is 0 = 90.0°. With a semimajor axis of a = (0.400 m)/2 and a semiminor axis of b = (0.300 m)/2, the area enclosed by th coil is A = nab = Tt m2, and the magnitude of the torque exerted on the coil is T = NBIAsin 0 ]a m2)sin 90.0° = 8 х 10-4 x 10¬4 N · m. %3D

The torque that a uniform magnetic field exerts on a flat (planar) coil is given by T = NBIAsin 0, where N is the number of turns of wire in the coil, B the magnitude of the magnetic field, I the current flowir in the coil, A the area enclosed by the coil, and 0 the angle between the line perpendicular to the plane of th coil and the direction of the magnetic field. The expression given above was derived for a rectangular coil bu 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 В |-30.0 cm-| d Thus, the angle between the magnetic field and the line perpendicular to the plane of the coil is 0 = 90.0°. With a semimajor axis of a = (0.400 m)/2 and a semiminor axis of b = (0.300 m)/2, the area enclosed by th coil is A = nab = Tt m2, and the magnitude of the torque exerted on the coil is T = NBIAsin 0 ]a m2)sin 90.0° = 8 х 10-4 x 10¬4 N · m. %3D

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter11: Magnetic Forces And Fields

Section: Chapter Questions

Problem 85AP: Acircularcoiofwireofradius5.Ocmhas2Otums and carries a current of 2.0 A. The coil lies in a magnetic...

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