A magnetic dipole with a dipole moment of magnitude 0.0306 J/T is released from rest in a uniform magnetic field of magnitude 57.6 mT. The rotation of the dipole due to the magnetic force on it is unimpeded. When the dipole rotates through the orientation where its dipole moment is aligned with the magnetic field, its kinetic energy is 0.573 mJ. (a) What is the initial angle between the dipole moment and the magnetic field? (b) What is the angle when the dipole is next (momentarily) at rest?

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A magnetic dipole with a dipole moment of magnitude 0.0306 J/T is released from rest in a uniform magnetic field of magnitude 57.6 mT. The rotation of the dipole due to the magnetic force on it is unimpeded. When the dipole rotates through the orientation where its dipole moment is aligned with the magnetic field, its kinetic energy is 0.573 mJ. (a) What is the initial angle between the dipole moment and the magnetic field? (b) What is the angle when the dipole is next (momentarily) at rest?

Expert Solution
Step 1

(a) Use conservation of energy to find the initial angle.

Ui-Uf=Kf-Ki-μBcosθi--μBcosθf=Kf-0-μBcosθi--μBcos0°=Kf-0-μBcosθi-1=Kf-0θi=cos-11-KfμB

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