Lecture_21_Part_1

Lecture_21_Part_1 - Magnetic Dipole Moment: Potential...

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A current carrying loop has a tendency to twist in magnetic field Compass needle: collection of atomic current loops B l I F m × Δ = Ihw IA = = μ Magnetic Torque on a Magnetic Dipole Moment
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B l I F m × Δ = IwB F m = θ sin IwB F = Torque ( τ ) = distance from the axle (lever arm) times perpendicular component of the force. τ sin sin 2 2 IwhB IwB h = = Ihw = μ sin B = B × = μ Works with loops of any shape! Magnetic Torque: Quantitative Analysis
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Calculate amount of work needed to rotate from angle θ I to θ f : dE = 2 F h 2 d θ = Δ = f i d h IwB U W m 2 sin 2 Δ U m = IwhB sin d i f = IwhB cos [ ] i f Δ U m = μ B cos f cos i cos B U m = Potential energy for a magnetic dipole moment B U m = Magnetic Dipole Moment: Potential Energy Ihw =
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Potential energy for a magnetic dipole moment B U m = μ U= min - µ B 0 max µ B 0 What is the energy difference between the highest and the lowest state? Picture of the U and µ in magnetic field – important in atomic and nuclear physics.
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Unformatted text preview: Magnetic Dipole Moment: Potential Energy B l Id F d = dF IBdl dF = dF sin IBdl dF = = dl IB F net sin sin 2 RIB F net = sin 2 R B F net = We dont know Force on a Magnetic Dipole B U m = 2 , 1 , m m U U < _ > = = B U x F m us by dx dB x B x U F m us by = = _ dx dU F x = dx dB F x = <0 There is no force if field is uniform! Force on a Magnetic Dipole F x = d ( i B ) dx x dx dB F x = 3 2 4 x B bar x 3 2 4 x dx d F bar x 4 6 4 x F bar x Two magnets 4 2 1 6 4 x F x Force on a Magnetic Dipole...
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Lecture_21_Part_1 - Magnetic Dipole Moment: Potential...

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