Electricity and Magnetism--Dipoles in Magnetic field

1 P17-Class 17: OutlineHour 1:Dipoles & Magnetic FieldsHour 2:Expt. 7: Dipoles in B Fields2 P17-Last Time:Biot-Savart3 P17-The Biot-Savart LawCurrent element of length dscarrying current Iproduces a magnetic field:20ˆ4rdIrsBd×=􀁇􀁇πµ2ˆx4oqrµπ=vrB􀁇􀁇Moving charges are currents too…(http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/03-CurrentElement3d/03-cElement320.html)4 P17-PRS Question:Force between wires5 P17-Magnetic Dipoles:Torque & Force6 P17-First: Review From Friday7 P17-Rectangular Current LoopPlace rectangular current loop in uniform B field ()BLFF􀁇􀁇􀁇􀁇I031==2ˆˆˆ()()IaBIaB=−×=Fjik􀁇4ˆˆˆ()()IaBIaB=×=−Fjik􀁇12340net=+=FFF+F+F􀁇􀁇􀁇􀁇􀁇ˆiˆjˆkNo net force on the loop!!8 P17-Torque on Rectangular Loop24ˆˆ22bb⎛⎞⎛⎞=−×+×⎜⎟⎜⎟⎝⎠⎝⎠τiFiF􀁇􀁇􀁇Frτ􀁇􀁇􀁇×=Torque Direction:Thumb in torque direction, fingers rotate with objectRecall:()()ˆˆˆˆ22bbIaBIaB⎛⎞⎛⎞=−×+×−⎜⎟⎜⎟⎝⎠⎝⎠ikikˆˆˆ22IabBIabBIabB=+=jjjˆiˆjˆkx9 P17-Torque on Rectangular LoopjτˆIAB=􀁇ˆˆ: area vectorAab==An n􀁇ˆˆˆ, =B=+nkBi􀁇ˆiˆjˆkxI=×τAB􀁇􀁇􀁇Familiar? No net force but there is a torque10 P17-Magnetic Dipole MomentAnµ􀁇􀁇IIA≡≡ˆDefine Magnetic Dipole Moment:=×τµB􀁇􀁇􀁇Then:Analogous to=×τpE􀁇􀁇􀁇τtends to align µwith B11 P17-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)12 P17-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.html13 P17-Demonstration:Galvanometer 14 P17-Magnetic Dipole MomentAnµ􀁇􀁇IIA≡≡ˆ15 P17-PRS Question:Torque on Dipole in Uniform Field16 P17-Dipoles don’t move???This dipole rotates but doesn’t feel a net forceBut dipoles CAN feel force due to B. What’s up?17 P17-PRS Question:Force on Magnetic Dipole18 P17-Something NewDipoles in Non-Uniform Fields: Force19 P17-Force on Magnetic Dipole -DipoleU=⋅µB􀁇􀁇To determine force, we need to know energy:() -DipoleDipoleU=∇=∇⋅FµB􀁇􀁇􀁇􀁇􀁇Force tells how the energy changes with position:()(after math)=⋅∇µB􀁇􀁇􀁇Dipoles only feel force in non-uniformfield20 P17-Force on Magnetic Dipole()Dipolezµ∂=⋅∇=∂BFµB􀁇􀁇􀁇􀁇􀁇negativeForce down!z∂∂B􀁇21 P17-Force on Magnetic DipoleAlternate ThoughtWhat makes the field pictured?22 P17-Force on Magnetic DipoleµNSNSBar magnet below dipole, with N pole on top It is aligned with the dipole pictured, they attract! 23 P17-Experiment 7:Magnetic Forces on Dipoles24 P17-Force on Dipole from Dipole:Anti-Parallel Alignmenthttp://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/16-MagneticForceRepel/16-MagForceRepel_f65_320.html25 P17-Force on Dipole from Dipole:Parallel Alignmenthttp://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/15-MagneticForceAttract/15-MagForceAtt_f65_320.html26 P17-PRS Questions:Force on Magnetic Dipole