A magnetic dipole with a dipole moment of magnitude 0.020 J/T is released from rest in a uniform...

Question

A magnetic dipole with a dipole moment of magnitude 0.020 J/T is released from rest in a uniform magnetic field of magnitude 52 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 0.80 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?

David · Accepted Answer

The expression for potential energy is given by
U = −µ · B = −|µ||B| cos θ
By Conservation of energy we have
Kf + Uf = Ki + Ui 
K − µB = 0 − µB cos θ
So we have 
Θ=arccos(1-K/ µB)
B)
This is similar to a ball falling through a valley. The ball will roll down the hill,

A magnetic dipole with a dipole moment of magnitude 0.020 J/T is released from rest in a uniform magnetic field of magnitude 52 mT. The rotation of the dipole due to the magnetic force on it is...

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