Class 17: OutlineLast Time:Biot-SavartThe Biot-Savart LawPRS Question:Force between wiresMagnetic Dipoles:Torque & ForceFirst: Review From FridayRectangular Current LoopTorque on Rectangular LoopTorque on Rectangular LoopMagnetic Dipole MomentAnimation:Another Way To Look At TorqueInteractive Java Applet:Another Way To Look At TorqueDemonstration:GalvanometerMagnetic Dipole MomentPRS Question:Torque on Dipole in Uniform FieldDipoles don’t move???PRS Question:Force on Magnetic DipoleSomething NewDipoles in Non-Uniform Fields: ForceForce on Magnetic DipoleForce on Magnetic DipoleForce on Magnetic DipoleForce on Magnetic DipoleExperiment 7:Magnetic Forces on DipolesForce on Dipole from Dipole:Anti-Parallel AlignmentForce on Dipole from Dipole:Parallel AlignmentPRS Questions:Force on Magnetic Dipole1P17-Class 17: OutlineHour 1:Dipoles & Magnetic FieldsHour 2:Expt. 7: Dipoles in B Fields2P17-Last Time:Biot-Savart3P17-The Biot-Savart LawCurrent element of length ds carrying current Iproduces a magnetic field:20ˆ4 rdI rsBd×=GGπµ2ˆx4oqrµπ=vrBGGMoving charges are currents too…(http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/03-CurrentElement3d/03-cElement320.html)4P17-PRS Question:Force between wires5P17-Magnetic Dipoles:Torque & Force6P17-First: Review From Friday7P17-Rectangular Current LoopPlace rectangular current loop in uniform B field ()BLFFGGGGI031==2ˆˆˆ()()Ia B IaB=− × =FjikG4ˆˆˆ()( )Ia B IaB=×=−Fji kG12340net=+=FFF+F+FGGG GGˆiˆjˆkNo net force on the loop!!8P17-Torque on Rectangular Loop24ˆˆ22bb⎛⎞ ⎛⎞=− × + ×⎜⎟ ⎜⎟⎝⎠ ⎝⎠τ iF iFGGGFrτGGG×=Torque Direction:Thumb in torque direction, fingers rotate with objectRecall:() ()ˆˆˆˆ22bbIaB IaB⎛⎞ ⎛⎞=− × + ×−⎜⎟ ⎜⎟⎝⎠ ⎝⎠iki kˆˆˆ22IabB IabBIabB=+=jjjˆiˆjˆkx9P17-Torque on Rectangular LoopjτˆIAB=Gˆˆ: area vectorAab==An nGˆˆˆ, =B=+nkBiGˆiˆjˆkxI=×τ ABGGGFamiliar? No net force but there is a torque10P17-Magnetic Dipole MomentAnµGGIIA ≡≡ˆDefine Magnetic Dipole Moment:=×τ µBGGGThen:Analogous to=×τ pEGGGτ tends to align µ with B11P17-Animation:Another Way To Look At TorqueExternal field connects to field of compass needle and “pulls” the dipole into alignment (http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/18-dipNeedle/18-Dip_320.html)12P17-Interactive Java Applet:Another Way To Look At TorqueField of wire connects to field of compass needle and “pulls” the dipole into alignmenthttp://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/35-wireandmagnetapp/35-wirecompass320.html13P17-Demonstration:Galvanometer14P17-Magnetic Dipole MomentAnµGGIIA ≡≡ˆ15P17-PRS Question:Torque on Dipole in Uniform Field16P17-Dipoles don’t move???This dipole rotates but doesn’t feel a net forceBut dipoles CAN feel force due to B. What’s up?17P17-PRS Question:Force on Magnetic Dipole18P17-Something NewDipoles in Non-Uniform Fields: Force19P17-Force on Magnetic Dipole -DipoleU=⋅µBGGTo determine force, we need to know energy:() -Dipole DipoleU=∇=∇⋅FµBGG GGGForce tells how the energy changes with position:()(after math) =⋅∇µBGGGDipoles only feel force in non-uniform field20P17-Force on Magnetic Dipole()Dipolezµ∂=⋅∇=∂BFµBGGGGGnegativeForce down!z∂∂BG21P17-Force on Magnetic DipoleAlternate ThoughtWhat makes the field pictured?22P17-Force on Magnetic DipoleµNSNSBar magnet below dipole, with N pole on top It is aligned with the dipole pictured, they attract!23P17-Experiment 7:Magnetic Forces on Dipoles24P17-Force on Dipole from Dipole:Anti-Parallel Alignmenthttp://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/16-MagneticForceRepel/16-MagForceRepel_f65_320.html25P17-Force on Dipole from Dipole:Parallel Alignmenthttp://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/15-MagneticForceAttract/15-MagForceAtt_f65_320.html26P17-PRS Questions:Force on Magnetic
View Full Document
Unlocking...