Lect13 - Physics 212 Le cture13 Torques 50 40 30 20 10 0...

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Unformatted text preview: Physics 212 Le cture13 Torques 50 40 30 20 10 0 Confused Avg = 3.0 Confident Physics 212 Le cture13, S 1 lide Music Who is the Artist? A) B) C) D) E) Jefferson Airplane Grateful Dead Moby Grape The Doors Cream Why? Why? I t ook a road trip last we ke and liste d to theGrate De e nd ne ful ad took channe on sate radio l llite channe I t’s be n awhile but it still sounds good !! e , Physics 212 Le cture13, S 2 lide Physics 212 Le cture13 Torques 50 40 30 20 10 0 Confused Avg = 3.0 Confident Physics 212 Le cture13, S 3 lide Ke C pts: y once • • Force & Torque on loops of curre dueto a m tic s s nt agne Force fie ld. f ie Them tic dipolem e agne om nt. Today’s Plan: • • • • Re w of cross product vie Force & Torque s s Magne dipolem e tic om nt Exam proble ple m 05 Physics 212 Le cture13, S 4 lide Last Tim : e r rr F = qv × B This Tim : e r rr F = q ∑ vi × B i z r r r F = qNvavg × B 06 rr r F = IL × B F I y B x Physics 212 Le cture13, S 5 lide ACT BB rr r F = IL × B A B C 08 Physics 212 Le cture13, S 6 lide Act BB rr r F = IL × B A B C 10 Physics 212 Le cture13, S 7 lide Act BB rr r F = IL × B What is the force on section d-a of the loop? A) Zero B) Out of the page C) Into the page 12 Physics 212 Le cture13, S 8 lide Pre flight 2 80 60 40 “Thene forceon any close loop is ze t d ro.” Check simulations if in doubt. 13 20 0 Physics 212 Le cture13, S 9 lide Pre flight 4 y x BB BB In which dire ction will theloop rotate ? (assum thez axis is out of thepage e ) (assum A) B) C) D) 15 Around thex axis Around they axis Around thez axis It will not rotate Physics 212 Le cture13, S 10 lide 10 Pre flight 6 BB R F rrr τ = R×F 30 25 20 15 10 5 0 17 Physics 212 Le cture13, S 11 lide 11 Magne DipoleMom nt tic e Area vector Magnitude = Area Direction uses R.H.R. Magnetic Dipole moment r r µ ≡ N IA 19 Physics 212 Le cture13, S 12 lide 12 µ Makes TorqueEasy! rrr τ = µ×B z Thetorquealways wants to line µ up with B ! rrr τ = µ × B turns µ toward B B y z µ x µ y x rrr τ = µ × B turns µ toward B B 21 Physics 212 Le cture13, S 13 lide 13 Practice with µ and τ rrr τ = µ×B µ I B I n this case µ is out of thepage(using right hand rule ) is z rrr τ = µ×B B y is up (turns µ toward B) t oward µ x 22 Physics 212 Le cture13, S 14 lide 14 Pre flight 8 100 rrr τ = µ×B rr Bigge whe µ ⊥ B st n 24 80 60 40 20 0 Physics 212 Le cture13, S 15 lide 15 Magne Fie can do Work on Curre tic ld nt From Physics 211: W = ∫τ dθ rrr From Physics 212: τ = µ × B = µ B sin(θ ) rr W = ∫ µ B sin(θ )dθ = µ B cos(θ ) = µ ⋅ B 1.5 ∆U = −W Define U = 0 at position of Define maximum torque maximum 1 0.5 0 0 -0.5 -1 -1.5 30 60 90 120 150 180 rr U ≡ −µ ⋅ B µ B Physics 212 Le cture13, S 16 lide 16 27 Pre flight 10 φ U = +µ Bcosφ U=0 U = -µ Bcosθ θ BB 50 rr U = −µ ⋅ B 40 30 20 10 0 30 Physics 212 Le cture13, S 17 lide 17 Pre flight 12 φa BY BY BY BY YOU FIELD YOU FIELD θa θc BY WHOM ?? Wby _ field = − ∆U = U i − U f rr U = −µ ⋅ B (C): (C): (b): (b): (a): (a): 30 Wby _ field = − µB − (− µB cosθ c ) = − µB (1 − cosθ c ) Wby _ field = − µB − 0 = − µB Wby _ field = − µB − (− µB cosθ a ) = − µB(1 + cos φa ) Physics 212 Le cture13, S 18 lide 18 C alculation A squareloop of sidea lie in thex-z planewith curre s nt I as shown. Theloop can rotateabout x axis without f riction. A uniformfie B points along the+z axis. ld Assum a, I , and B areknown. e How m doe thepote uch s ntial e rgy of thesyste ne m changeas thecoil m s fromits initial position to its ove f inal position. a I x z z B 30˚ . B y y initial final once • C ptual Analysis nt ay xpe nce agne ld – A curre loop m e rie a torquein a constant m tic fie τ = µ XB • ntial e rgy with theorie ne ntation of loop – Wecan associatea pote • U =- µ ∙B trate • S gic Analysis – Find µ ntial e rgy frominitial to final ne – Calculatethechangein pote 32 Physics 212 Le cture13, S 19 lide 19 C alculation A squareloop of sidea lie in thex-z planewith curre s nt I as shown. Theloop can rotateabout x axis without f riction. A uniformfie B points along the+z axis. ld Assum a, I , and B areknown. e a I x z z B 30˚ . B y y initial final ction of them tic m e of this curre loop in its initial position? agne om nt nt • What is thedire (A) +x (A) (B) -x z (C +y ) z (D) -y . x ● y rr µ = IA X µ y Right Hand Rule 34 Physics 212 Le cture13, S 20 lide 20 C alculation A squareloop of sidea lie in thex-z planewith curre s nt I as shown. Theloop can rotateabout x axis without f riction. A uniformfie B points along the+z axis. ld Assum a, I , and B areknown. e a I x z z B 30˚ . B y y initial final ction of thetorqueon this curre loop in theinitial position? nt • What is thedire (A) +x (A) (B) -x z (C +y ) B (D) -y . X µ y 36 Physics 212 Le cture13, S 21 lide 21 C alculation A squareloop of sidea lie in thex-z planewith curre s nt I as shown. Theloop can rotateabout x axis without f riction. A uniformfie B points along the+z axis. ld Assum a, I , and B areknown. e a z z B 30˚ . B y y rr U = −µ ⋅ B ntial e rgy of theinitial state ne ? • What is thepote (A) Uinitial < 0 (B) Uinitial = 0 z B I x initial final (C Uinitial > 0 ) θ = 900 µ y θ rr µg = 0 B 38 Physics 212 Le cture13, S 22 lide 22 C alculation A squareloop of sidea lie in thex-z planewith curre s nt I as shown. Theloop can rotateabout x axis without f riction. A uniformfie B points along the+z axis. ld Assum a, I , and B areknown. e a z z B 30˚ . B y y rr U = −µ ⋅ B ntial e rgy of thefinal state ne ? • What is thepote (A) Ufinal < 0 (B) Ufinal = 0 z z I x initial final (C) Ufinal > 0 initial B B f inal θ = 90 + 30 ο θ = 1200 y θ = 90 µ 40 rr µg < 0 B y ο ο µ rr U = −µ ⋅ B > 0 Physics 212 Le cture13, S 23 lide 23 C alculation A squareloop of sidea lie in thex-z planewith curre s nt I as shown. Theloop can rotateabout x axis without f riction. A uniformfie B points along the+z axis. ld Assum a, I , and B areknown. e z z B 30˚ . B rr U = −µ ⋅ B ntial e rgy of thefinal state ne ? • What is thepote (A) U = Ia B (B) (A) 2 a I x y initial final 3 U = (C) 2 B Ia 2 z cos(120o ) = − B 1 2 θ = 120 ο rr 1 o U = − µ ⋅ B = − µ B cos(120 ) = µ B 2 µ = Ia 2 U= 12 Ia B 2 Physics 212 Le cture13, S 24 lide 24 12 U = Ia B 2 y µ 44 ...
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