1 W07D1 Magnetic Dipoles, Force and Torque on a Dipole, Experiment 2 W07D1 Magnetic Dipoles, Torque and Force on a Dipole, Experiment 2: Magnetic Dipole in a Helmholtz Coil http://web.mit.edu/8.02t/www/materials/Experiments/expMagForcesDipoleHelmholtz.pdf Reading Course Notes: Sections 8.4, 8.6.4, 8.10.4, 8.13, 9.5, 9.9Announcements Exam Two Reviews: Tuesday from 7:30-9 pm in 26-152 Tuesday from 9-10:30 pm in 26-152 PS 6 due W07 Tuesday at 9 pm in boxes outside 32-082 or 26-152 Exam 2 Thursday March 20 7:30 - 9:30 pm: See announcement pages for section room assignments Conflict Friday March 21 8-10 am and 10-12 noon in 32-082 23 Magnetic Field of Bar Magnet (1) A magnet has two poles, North (N) and South (S) (2) Magnetic field lines leave from N, end at S4 Demonstration: Magnetic Field Lines from Bar Magnet G2 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%202&show=05 Magnetism – Bar Magnet Like poles repel, opposite poles attract6 Bar Magnets Are Dipoles! NO! Magnetic monopoles do not exist in isolation • Create Dipole Field • Rotate to orient with Field Is there magnetic “mass” or magnetic “charge?”7 Magnetic Monopoles? Magnetic monopoles do not exist in isolation q -q pElectric Dipole When cut: 2 monopoles (charges) µMagnetic Dipole When cut: 2 dipoles Another Maxwell’s Equation! (2 of 4) E ⋅ dAS∫∫=qinε0 B ⋅ dAS∫∫= 0Gauss’s Law Magnetic Gauss’s Law8 Conservation of Magnetic Flux: E ⋅ dAS∫∫=qinε0 B ⋅ dAS∫∫= 09 Concept Question: Magnetic Field Lines The picture shows the field lines outside a permanent magnet The field lines inside the magnet point: 1. Up 2. Down 3. Left to right 4. Right to left 5. The field inside is zero 6. I don’t know10 Animation: Magnetic Field Generated by a Current Loop http://web.mit.edu/viz/EM/visualizations/magnetostatics/calculatingMagneticFields/RingMagInt/RingMagIntegration.htmMagnetic Dipole Moment µ≡ IAˆn ≡ IAhttp://web.mit.edu/viz/EM/visualizations/magnetostatics/calculatingMagneticFields/RingMagField/RingMagField.htmIf the wire is a uniform magnetic field then If the wire is also straight then 12 Review: Magnetic Force on Current-Carrying Wire Fmag= I dswire∫⎛⎝⎜⎞⎠⎟×B Fmag= I (L ×B)13 Torque on a Current Loop in a Uniform Magnetic Field14 Group Problem: Current Loop Place rectangular current loop in uniform B field ˆiˆjˆk1) What is the net force on this loop? 2) What is the net torque on this loop? 3) Describe the motion the loop makes15 Torque on Rectangular Loop A = Aˆn = abˆn τ = IA ×B ˆn = +ˆk, B=Bˆi τ = IABˆjNo net force but there is a torque ˆiˆjˆkx Area vector16 Torque on Current Loop Place rectangular current loop in uniform B field ˆiˆjˆk Magnetic moment points out of the page torque tries to align the magnetic moment vector in the direction of the magnetic field µ τ =µ ×B τ =µ ×B =µBˆj = IABˆj17 Demonstration: Deflection of a Compass Needle by a Magnet G1 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%201&show=018 Demonstration: Galvanometer principle G10 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%2010&show=019 Concept Question: Dipole in Field From rest, the coil above will: 1. rotate clockwise, not move 2. rotate counterclockwise, not move 3. move to the right, not rotate 4. move to the left, not rotate 5. move in another direction, without rotating 6. both move and rotate 7. neither rotate nor move 8. I don’t know µ20 Force on a Dipole in a Non-Uniform Field21 Dipoles don’t move??? This dipole rotates but doesn’t feel a net force in a uniform magnetic field But dipoles can feel magnetic force.22 Dipoles in Non-Uniform Fields: Magnetic Force23 Concept Question: Dipole in Field The current carrying coil above will feel a net force 1. upwards 2. downwards 3. of zero 4. I don’t knowN S 24 Force on Magnetic Dipole What makes the field pictured? Bar magnet below dipole, with N pole on top. It is aligned with the dipole pictured, they attract! N S µWork Done by Interaction to Anti-align Magnetic Dipole 25 W =τzdθ0π∫= −µB sinθdθ0π∫=µB cosθ0π= −2µB τ =µ ×B = -µB sinθˆk =τzˆkPotential Energy: Dipole in Magnetic Field 26 ΔU = U (θ=π) − U (θ= 0) = −W = 2µB = −µθ=π⋅BSet zero reference point U (θ=π/ 2) = 0 U (θ) = −µ⋅BLowest energy state (aligned) : U (θ= 0) = −µBHighest energy state (anti-aligned): U (θ=π) =µB27 Force on Magnetic Dipole N S N S UDipole= -µ ⋅B F = −∇(− µ ⋅B) ⇒F =∇( µ ⋅B)Fz(0,0, z) =µz∂Bz∂z µ ↑Experiment 2: Magnetic Forces on Dipole in Fields of Helmholtz CoilGetting Started: Set up current supply • Open circuit (disconnect a lead) • Turn current knob full CCW (off) • Increase voltage to ~12 V – This will act as a protection: V<12 V • Reconnect leads in Helmholtz mode • Increase current to ~1 AAppendix Experiment 2: Magnetic Forces on Dipole in Fields of Helmholtz Coil Field Configurations and Concept QuestionsMagnetic Field Profiles for Experiment 2Concept Question: Dipole in Helmholtz A dipole pointing along the positive x-direction and located at the center of a Helmholtz coil will feel: 1. a force but not a torque. 2. a torque but not a force. 3. both a torque and a force. 4. neither force nor torque.Concept Question: Dipole in Anti-Helmholtz Coil A dipole pointing along the positive z-direction and located at the center of an anti- Helmholtz coil will feel: 1. a force but not a torque. 2. a torque but not a force. 3. both a torque and a force. 4. neither force nor
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