Gyromagnetic Ratio For A Classical Rotating Body
Consider a charged body rotating about an axis of symmetry. According to the laws of classical physics, it has both a magnetic dipole moment and an angular momentum due to its rotation. It can be shown that as long as its charge and mass are distributed identically (e.g., both distributed uniformly), its gyromagnetic ratio is
where q is its charge and m is its mass. The derivation of this relation is as follows:
It suffices to demonstrate this for an infinitesimally narrow circular ring within the body, as the general result follows from an integration. Suppose the ring has radius r, area A = πr2, mass m, charge q, and angular momentum L=mvr. Then the magnitude of the magnetic dipole moment is
as desired.
Read more about this topic: Gyromagnetic Ratio
Famous quotes containing the words ratio, classical and/or body:
“Official dignity tends to increase in inverse ratio to the importance of the country in which the office is held.”
—Aldous Huxley (1894–1963)
“Against classical philosophy: thinking about eternity or the immensity of the universe does not lessen my unhappiness.”
—Mason Cooley (b. 1927)
“When my body leaves me
I’m lonesome for it.
but body
goes away to I don’t know where
and it’s lonesome to drift
above the space it
fills when it’s here.”
—Denise Levertov (b. 1923)