Nuclear Precession
Where does the energy come from to keep the precession going?
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Surprisingly, no energy is required to keep the precession of an individual proton going. The reason for this is not immediately obvious but can be understood by considering the energetics of a precessing gyroscope.
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The gyroscope pictured above is precessing in a circle parallel to the floor and perpendicular to the earth's gravitational field. Although precessing, the center of mass of the gyroscope remains unchanged in height from the floor. The gyroscope's potential energy is directly proportional to the height of its center of gravity. Since this height remains constant during the precession, no change in energy occurs.
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A similar explanation can be used to demonstrate that a magnet (AKA nuclear spin) does not undergo energy exchange during simple precession.
The diagram to the left shows a small magnet (here, a compass needle) aligned with, against, or at an angle to the external magnetic field (Bo). |
The lowest energy state of the system is when the needle is aligned with Bo. To twist the needle in the opposite direction requires the input of energy (like pushing it with your finger). The opposed state thus has a higher energy level than the aligned state.
During precession, the angle of orientation of the needle with respect to the external field does not change. Hence energy is neither gained nor lost. The Bo field serves to sustain the precession, but does not create the precession nor contribute energy to maintain it.
During precession, the angle of orientation of the needle with respect to the external field does not change. Hence energy is neither gained nor lost. The Bo field serves to sustain the precession, but does not create the precession nor contribute energy to maintain it.
References
Butikov E. Precession and nutation of a gyroscope (pdf). Also from this link (accessed 2016).
Butikov E. Precession and nutation of a gyroscope (pdf). Also from this link (accessed 2016).