Lect15 - Physics 212 rr B ⋅ d l = µ0 I enclosed Ñ 40 30 20 Le cture15 Am re Law pe ’s 10 0 Confused Avg = 3.2 Confident Physics 212 Le

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Unformatted text preview: Physics 212 rr B ⋅ d l = µ0 I enclosed Ñ ∫ 40 30 20 Le cture15 Am re Law pe ’s 10 0 Confused Avg = 3.2 Confident Physics 212 Le cture15, S 1 lide Music ho is the Artist? ) ) ) ) ) Albert Collins Buddy Guy Coco Montoya John Mayall Tommy Castro BB Oneof m favoriteblue guitar playe y s rs One Hedoe a gre liveshow at He s S d out as drum e for Albe C tarte mr rt ollins Also playe in Blue ake with John Mayall d sbre rs Physics 212 Le cture15, S 2 lide Physics 212 rr B ⋅ d l = µ0 I enclosed Ñ ∫ 40 30 20 Le cture15 Am re Law pe ’s 10 0 Confused Avg = 3.2 Confident Physics 212 Le cture15, S 3 lide Infinite current-carrying wire B 2π r = µ 0 I µ0 I B= 2πr :05 Physics 212 Lecture 15, Slide 4 Preflight 2 80 60 40 which is the same in both cases. which :08 rr ∫ B ⋅ d l only depends on the current enclosed, 20 0 Physics 212 Lecture 15, Slide 5 Preflight 4 100 80 60 40 :09 In case 2, the loop does not enclose any current, so integral b.dl is zero. And in case 1, the loop does enclose current and therefore the value is non zero. 20 0 Physics 212 Lecture 15, Slide 6 Preflight 6 Enclosed current = 0 For both cases 70 60 50 40 30 20 10 0 :09 Physics 212 Lecture 15, Slide 7 Preflight 8 Cylindrical Symmetry X X X X BB Enclosed Current = 0 Check cancellations 50 40 30 20 10 0 :22 Physics 212 Lecture 15, Slide 8 Ampere’s Law I into screen rr Ñ ⋅ dl = µ0 I enc ∫B Physics 212 Lecture 15, Slide 9 :12 Ampere’s Law rr Ñ ⋅ dl = µ0 I enc ∫B dl B B dl :14 B dl Physics 212 Lecture 15, Slide 10 10 Ampere’s Law rr Ñ ⋅ dl = µ0 I enc ∫B dl B B dl :16 dl B Physics 212 Lecture 15, Slide 11 11 Ampere’s Law rr Ñ ⋅ dl = µ0 I enc ∫B dl B B dl B dl :16 Physics 212 Lecture 15, Slide 12 12 Which of thefollowing curre distributions nt Which would giveriseto theB.dL distribution at the would dL right? right? BB A :18 B C Physics 212 Le cture15, S 13 lide 13 :19 Physics 212 Le cture15, S 14 lide 14 :19 Physics 212 Le cture15, S 15 lide 15 :19 Physics 212 Le cture15, S 16 lide 16 Match theothe two: r A B BB :21 Physics 212 Le cture15, S 17 lide 17 Preflight 10 80 60 40 Use the right hand rule and curl your Use fingers along the direction of the current. current. :22 20 0 Physics 212 Lecture 15, Slide 18 18 Simulation :23 Physics 212 Lecture 15, Slide 19 19 S noid ole S ve loops packe tightly toge r forma uniformm tic fie inside and ne ze e ral d the agne ld , arly ro m tic fie outside agne ld . 1 2 rr Ñ ⋅ dl = µ0 I enc ∫B 2 1 2 3 4 3 r r 3r r 4r r 1r r ∫ B ⋅d l + ∫ B ⋅d l + ∫ B ⋅d l + ∫ B ⋅d l = µ0 I enc 4 BL + 0 + 0 + 0 = µ 0 I enc BL = µ0 nLI :28 B = µ0 nI Physics 212 Lecture 15, Slide 20 20 Exam Proble ple m An infinitely long cylindrical shell with inner radius a and outer radius b carries a uniformly distributed current I into the screen. Sketch |B| as a function of r. a y I x once • C ptual Analysis om te m try pe – C ple cylindrical sym e (can only de nd on r) ⇒ can useAm re law to calculateB pe ’s ld , rclockwiseor ze ro! – B fie can only beclockwise counte b rr Ñ ⋅ dl = µ0 I enc ∫B r r B Ñ = µ 0 I enc For circular path concentric w/ shell ∫ dl trate • S gic Analysis C alculateB f or thethre re e gions se parate ly: 1) r < a 2) a < r < b 3) r > b Physics 212 Lecture 15, Slide 21 21 :31 Exam Proble ple m r y I a b BB x What doe | B| look likefor r < a ? s rr Ñ ⋅ dl = µ0 I enc ∫B 0 r so B = 0 (A) (A) :33 (B) (B) (C) (C) Physics 212 Le cture15, S 22 lide 22 Exam Proble ple m r What doe | B| look likefor r > b ? s y I a b BB x rr Ñ ⋅ dl = µ0 I enc ∫B I (A) (A) :35 (B) (B) (C) (C) Physics 212 Le cture15, S 23 lide 23 Exam Proble ple m dl B What doe | B| look likefor r > b ? s r y I a b x rr Ñ ⋅ dl = µ0 I ∫B Ñ ∫ Bdl BÑ ∫ dl B 2π r B 2π r = µ0 I µ0 I B= 2π r :36 Physics 212 Le cture15, S 24 lide 24 Exam Proble ple m r What doe | B| look likefor r > b ? s y I a b x B= µ0 I 2π r (A) (A) :37 (B) (B) (C) (C) Physics 212 Le cture15, S 25 lide 25 Exam Proble ple m y I What is thecurre de nt nsity j (Am 2) in theconductor? p/m a b BB x (A) (A) I (B) j = 2 (B) πb I j = 2 (C) 2 (C) πb +πa I j= 2 2 πb −πa :40 Physics 212 Le cture15, S 26 lide 26 Exam Proble ple m y I What is thecurre de nt nsity j (Am 2) in theconductor? p/m a b x j = I / area area = π b 2 − π a 2 I j= 2 2 πb −πa :41 Physics 212 Le cture15, S 27 lide 27 Exam Proble ple m y I What is thecurre de nt nsity j (Am 2) in theconductor? p/m a b x (A) (A) I (B) j = 2 (B) πb I j = 2 (C) 2 (C) πb +πa I j= 2 2 πb −πa :42 Physics 212 Le cture15, S 28 lide 28 Exam Proble ple m r What doe | B| look likefor a < r < b ? s y I a b BB x (A) (A) :43 (B) (B) (C) (C) Physics 212 Le cture15, S 29 lide 29 Exam Proble ple m r What doe | B| look likefor a < r < b ? s y I a b x rr Ñ ⋅ dl = µ0 I enc ∫B 2π rB = µ0 j areaencloses 2 2 areaenc = π r 2 − π a 2 I 2π rB = µ0 ( π r − π a ) × π b2 − π a 2 ) ( B = µ0 :45 (πr 2 −πa ) I × 2π r π b2 − π a 2 ) ( 2 S tarts at 0 and incre s ase alm line ost arly Physics 212 Le cture15, S 30 lide 30 Exam Proble ple m r What doe | B| look likefor a < r < b ? s y I a b x (A) (A) :46 (B) (B) (C) (C) Physics 212 Le cture15, S 31 lide 31 Exam Proble ple m An infinite long cylindrical she with inne radius a and oute radius ly ll r r b carrie a uniform distribute curre I out of the screen. s ly d nt S tch | B| as a function of r. ke a y I x b :48 Physics 212 Lecture 15, Slide 32 32 Follow-Up Add an infinitewirealong thez axis carrying curre I 0. nt a y I I0 X BB x What m betrueabout I 0 such that the is som valueof r, a < r < b, ust re e such that B(r) = 0 ? A) |I0| > |I| AND I0 into screen A) |I B) |I0| > |I| AND I0 out of screen B) |I C) |I0| < |I| AND I0 into screen C) |I D) |I0| < |I| AND I0 out of screen D) |I b E) There is no current I0 that can produce B = 0 there E) There B will be zero if total current enclosed = 0 :48 Physics 212 Lecture 15, Slide 33 33 ...
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This note was uploaded on 03/05/2011 for the course PHYS 212 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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