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Magnetostriction is the physical size change of magnetostrictive metals when in the presence of a magnetic field. As an example, when 50Hz or 60Hz lighting "hums" this is caused by magnetostriction.
As an example of a sensor, specifically optical fiber sensors, you would fix a length of fiber to a magnetostrictive material and measure the phase shift of the signal relative to the length change of the fiber due to the strength of the field.
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