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Unformatted text preview: Physics 225/315 February 8, 2008 Fictitious Magnetic Field Rotating frames We have seen the expression for the rate of change of a vector which is rotating. dA dt = ω × A The relationship between the rate of change of a vector in the Lab frame of reference and in a rotating frame (angular frequency = ω ) is. dA dt Lab = ∂A ∂t Rot + ω × A Rotating Spin We will apply this to the spin and magnetic moment vectors which are rotating around a fixed magnetic field, B in the Lab system. ∂S ∂t Rot = dS dt Lab ω × S ∂S ∂t Rot = γS × B + S × ω ∂S ∂t Rot = S × ‡ γB + ω · = γS × ˆ B + ω γ ! = γS × B eff ∂M ∂t Rot = γM × B eff Compare with the original expression in the Lab frame dM dt = γM × B ω γ = B fict B eff = B + B fict In the rotating frame the effective magnetic field which acts on the magnetic moment is B eff which is the sum of the real field...
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This note was uploaded on 03/01/2010 for the course PHYSICS 225 taught by Professor Rothberg during the Spring '10 term at University of Washington.
 Spring '10
 ROTHBERG
 Physics

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