Physics 1502: Lecture 20 Today s Agenda
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1 Physics 152: Lecure 2 Today s Agenda Announcemens: Chap.27 & 28 Homework 6: Friday nducion Faraday's Law ds N S v S N v 1
2 A Loop Moving Through a Magneic Field ε() =? F() =? Φ() =? Schemaic Diagram of an AC Generaor ε = Ν dφ d d (cos( ω)) = ΝΑΒ d = ΝΑΒ ω sin( ω)) 2
3 Schemaic Diagram of an DC Generaor 3
4 (a) As he conducing plae eners he field (posiion 1), he eddy currens are counerclockwise. As he plae leaves he field (posiion 2), he currens are clockwise. n eiher case, he force on he plae is opposie o he velociy, and evenually he plae comes o res. (b) When slos are cu in he conducing plae, he eddy currens are reduced and he plae swings more freely hrough he magneic field. Demo E-M Cannon Connec solenoid o a source of alernaing volage. The flux hrough he area o axis of solenoid herefore changes in ime. A conducing ring placed on op of he solenoid will have a curren induced in i opposing his change. There will hen be a force on he ring since i conains a curren which is circulaing in he presence of a magneic field. v side view F F op view ~ 4
5 Lecure 2, ACT 1 Suppose wo aluminum rings are used in he demo; Ring 2 is idenical o Ring 1 excep ha i has a small sli as shown. Le F 1 be he force on Ring 1; F 2 be he force on Ring 2. (a) F 2 < F 1 (b) F 2 = F 1 (c) F 2 > F 1 Lecure 2, ACT 2 Suppose one copper and one aluminum rings are used in he demo; he resisance of he wo rings is similar bu he aluminum ring has less mass. Le a 1 be he acceleraion of ring 1 and a 2 be he acceleraion of Ring 2. Ring 1 Ring 2 (a) a 2 < a 1 (b) a 2 = a 1 (c) a 2 > a 1 5
6 Lecure 2, ACT 3 Suppose you ake he aluminum ring, shoo i off he cannon, and ry o nail your annoying neighbor. Unforunaely, you jus miss. You hink, maybe can hi him (her) if change he emperaure of he ring. n order o hi your neighbor, do you wan o hea he ring, cool he ring, or is i jus hopeless? (a) hea (b) cool (c) hopeless Ho Ring Cool Ring Lecure 2, ACT 4 Suppose he alernaing magneic field is kep a a level where he ring jus leviaes, bu doesn jump off. f keep he ring suspended for abou 5 minues, is i safe o pick i up? (a) No (b) Yeah, ll do i ~ side view 6
7 nducion Self-nducance, RL Circuis X X X X X X X X X ε L/R V L Recap from he las Chaper: Faraday's Law of nducion N S v S N v Time dependen flux is generaed by change in magneic field srengh due moion of he magne Noe: changing magneic field can also be produced by ime varying curren in a nearby loop Can ime varying curren in a conducor induce EMF in in ha same conducor? d/d 7
8 Self-nducance Consider he loop a he righ. swich closed curren sars o flow in he loop. magneic field produced in he area enclosed by he loop. flux hrough loop changes X X XX X X X X XX X X XX emf induced in loop opposing iniial emf Self-nducion: he ac of a changing curren hrough a loop inducing an opposing curren in ha same loop. Self-nducance The magneic field produced by he curren in he loop shown is proporional o ha curren. The flux, herefore, is also proporional o he curren. We define his consan of proporionaliy beween flux and curren o be he inducance L. We can also define he inducance L, using Faraday's Law, in erms of he emf induced by a changing curren. 8
9 Self-nducance The inducance of an inducor ( a se of coils in some geomery, e.g., solenoid, oroid) hen, like a capacior, can be calculaed from is geomery alone if he device is consruced from conducors and air. f exra maerial (e.g. iron core) is added, hen we need o add some knowledge of maerials as we did for capaciors (dielecrics) and resisors (resisiviy) 9
10 Self-nducance The inducance of an inducor ( a se of coils in some geomery..eg solenoid, oroid) hen, like a capacior, can be calculaed from is geomery alone if he device is consruced from conducors and air. f exra maerial (eg iron core) is added, hen we need o add some knowledge of maerials as we did for capaciors (dielecrics) and resisors (resisiviy) S UNTS for L : Henry Archeypal inducor is a long solenoid, jus as a pair of parallel plaes is he archeypal capacior. r << l Long Solenoid: Calculaion N urns oal, radius r, Lengh l l r N urns For a single urn, The oal flux hrough solenoid is given by: nducance of solenoid can hen be calculaed as: This (as for R and C) depends only on geomery (maerial) 1
11 RL Circuis A =, he swich is closed and he curren sars o flow. a b Loop rule: L Noe ha his eqn is idenical in form o ha for he RC circui wih he following subsiuions: RC: RC RL: Lecure 2, ACT 5 A = he swich is hrown from posiion b o posiion a in he circui shown: 1A Wha is he value of he curren a long ime afer he swich is hrown? (a) = (b) = ε / 2R (c) = 2ε / R 1 Wha is he value of he curren immediaely afer he swich is hrown? (a) = (b) = ε / 2R (c) = 2ε / R 11
12 Lecure 2, ACT 5 A = he swich is hrown from posiion b o posiion a in he circui shown: 1A Wha is he value of he curren a long ime afer he swich is hrown? (a) = (b) = ε / 2R (c) = 2ε / R 1 Wha is he value of he curren immediaely afer he swich is hrown? (a) = (b) = ε / 2R (c) = 2ε / R RL Circuis To find he curren as a fc of ime, we need o choose an exponenial soluion which saisfies he boundary condiion: a b L We herefore wrie: The volage drop across he inducor is given by: 12
13 RL Circui (ε on) Curren ε/r L/R 2L/R Max = ε/r 63% Max a =L/R Volage on L ε Max = ε/r 37% Max a =L/R V L RL Circuis Afer he swich has been in posiion a for a long ime, redefined o be =, i is moved o posiion b. Loop rule: a b L The appropriae iniial condiion is: The soluion hen mus have he form: 13
14 RL Circui (ε off) Curren ε/r L/R 2L/R Max = ε/r 37% Max a =L/R Volage on L Max = -ε 37% Max a =L/R V L -ε ε on ε off ε/r L/R 2L/R ε/r L/R 2L/R ε V L V L -ε 14
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Chaper 0 NDUCTANCE Recommended Problems: 3,5,7,9,5,6,7,8,9,,,3,6,7,9,3,35,47,48,5,5,69, 7,7. Self nducance Consider he circui shown in he Figure. When he swich is closed, he curren, and so he magneic field,
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