ch28-p053 - 53. We use Eq. 28-37 where is the magnetic...

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53. We use Eq. 28-37 where G µ is the magnetic dipole moment of the wire loop and G B is the magnetic field, as well as Newton’s second law. Since the plane of the loop is parallel to the incline the dipole moment is normal to the incline. The forces acting on the cylinder are the force of gravity mg , acting downward from the center of mass, the normal force of the incline F N , acting perpendicularly to the incline through the center of mass, and the force of friction f , acting up the incline at the point of contact. We take the x axis to be positive down the incline. Then the x component of Newton’s second law for the center of mass yields mg f ma sin . θ = For purposes of calculating the torque, we take the axis of the cylinder to be the axis of rotation. The magnetic field produces a torque with magnitude B sin , and the force of
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