MASSACHUSETTS INSTITUTE OF TECHNOLOY Deparmen of Physics 8.02 Spring 2005 OBJECTIVES Experimen 9: Faraday s Law of Inducion 1. To become familiar wih he conceps of changing magneic flux and induced curren associaed wih Faraday s Law of Inducion. 2. To see how and why he direcion of he magneic force on a conducor carrying an induced curren is consisen wih Lenz s Law. Lenz s Law says ha he sysem always responds so as o ry o keep hings he same. OUTLINE This experimen consiss of hree pars: 1. Predicion of he magneic flux hrough a closed conour and he direcion of he induced curren in a wire along his conour associaed wih he change of his flux wih ime as he wire moves, using Faraday s Law. 2. Qualiaive measuremen of he curren and flux, and he relaionship beween hese wo. 3. Qualiaive deerminaion of he direcion of he force on a curren-carrying conducor due o he induced curren in a magneic field. Par 1: Predicions of Magneic Flux and Induced Curren The quesions for Par 1 refer o he four graphs below. Each graph is a qualiaive depicion of some physical quaniy as a funcion of ime. To answer he quesions, refer o he numbers ha label each of he graphs. Ener your predicions on he ear-shee a he end of hese insrucions. (1) (2) E09-1
(3) (4) In his exercise we predic he ime dependence of he curren in a coil as he coil is moved up and down pas a saionary permanen magne. The coil and magne are arranged as in he figure below. The Norh Pole of he magne is on he op. da N Predicion 1-1: Suppose you move he loop from well above he magne o well below he magne a a consan speed. Predic he shape of a graph of he magneic flux hrough he loop as a funcion of ime, aking he direcion of da= danˆ for he loop as upward. Predicion 1-2: Suppose you move he loop from well above he magne o well below he magne a consan speed. Predic he shape of a graph of he curren hrough he loop as a funcion of ime, aking he posiive direcion for curren in he loop o be couner-clockwise when viewed looking down on he apparaus from above. Predicion 1-3: Now suppose you move he loop from well below he magne o well above he magne a a consan speed. Predic he shape of a graph of he magneic flux hrough he loop as a funcion of ime, aking he direcion of da= danˆ for he loop as upward. Predicion 1-4: Now suppose you move he loop from well below he magne o well above he magne a consan speed. Predic he shape of he curren hrough he loop E09-2
as a funcion of ime, aking he posiive direcion of curren in he loop as counerclockwise when viewed looking down on he apparaus from above. Par 2: Measuremens of Induced Volage, Induced Curren and Flux Download he exp09.ds DaaSudio file from he "Curren Assignmen" Web Page. The aciviy is already se up o graph induced curren and magneic flux as funcions of ime. Take he coil of wire from your experimenal se-up, connec i o he Curren Sensor and connec he Curren Sensor o Analog Channel A on he Science Workshop 750 Inerface (hese las wo seps may be done for you already). Recall he convenion for he Curren Sensor and DaaSudio, ha he direcion of posiive curren hrough he Curren Sensor is from red o black. To allow he correc inerpreaion of he sign of he curren, carefully examine he way he wire loops in your coil. The leads should be conneced so ha hey lead from he black erminal on he Curren Sensor o he coil, around he coil in a counerclockwise direcion as viewed from above and hen back o he red erminal on he Curren Sensor. There is an arrow on he Curren Sensor o remind you of his convenion. Perform he wo moions indicaed above, and check your Predicions 1-1 hrough 1-4 for he curren and he magneic flux. The DaaSudio aciviy is se o sample daa for a ime inerval of 2 seconds a a rae of 100 samples per second (100 herz). A recommended procedure is o sar wih he coil a he op of he plasic ube, begin aking daa by pressing Sar, and moving he coil downward as evenly (uniform speed) as you can over he inerval of 2 seconds. Then repea, moving he coil up. DaaSudio should plo he wo measuremens on he same axes, allowing fairly easy comparison. Make he scale fi each of he graphs in he window by clicking on he icon a he upper lef of he graph window. If somehing doesn work righ he firs ime, or even he second, go o Experimen from he main menu and selec Delee ALL Daa Runs. Anoher suggesion is o lif or lower he alligaor clips ha are conneced o he coil as you move he coil up or down; his will preven having he clips come off he wire coil or hiing he magne (he clips are magneic). Quesion 1 (answer on your ear-off shee a he end): Did your predicions agree wih your measuremens? A Noe On How We Measure Magneic Flux: When you use he DaaSudio Aciviy, he op panel of he graph window will show he measuremen of I (), and he boom panel will be labeled Field Flux. Here we explain how he values displayed on he boom panel compued. We know from Faraday s Law ha when an ohmic resisor of resisance R coincides wih he loop ha bounds he surface hrough which he magneic flux is deermined for Faraday s Law, E09-3
d IR = Φ mag, d and since we measure I (),we can compue Φ mag () by numerically inegraing; R I ( ) Φ () = d mag 0. The DaaSudio sofware is capable of inegraing I ( ) and displaying he inegral a he same ime ha I () is measured, and he inegral is wha is displayed in he boom plo. Quesion 2 (answer on your ear-off shee a he end): Noe ha no maer how quickly or slowly you move he coil up and down pas he magne, as long as you go from far above o far below, or from far below o far above, he magniude of he flux funcion will always aain he same maximum value in he process. Why? Par 3: Feel he ( Id s B ) Force! The force on a segmen ds of a wire carrying curren I in a magneic field given by df = I d s B ex B ex is Noe ha ds here has a physical meaning: he direcion of he curren flow. In he wo preceding figures, he posiive direcion for curren flow was deermined purely mahemaically by our choice of direcion for da = da nˆ. Noe also ha B ex is he magneic field produced by exernal currens somewhere else, such as he aomic currens in he permanen magne; i is no he magneic field of he wire segmen iself. Ener your predicions on he ear-shee a he end of hese insrucions. E09-4
Predicion 3-1: Suppose you move he loop from well above he magne o well below flow when he loop is above he magne, should he direcion of he magneic force poin up or down? Predicion 3-2: Suppose you move he loop from well above he magne o well below flow when he loop is below he magne, should he direcion of he magneic force poin up or down? Predicion 3-3: Suppose you move he loop from well below he magne o well above flow when he loop is below he magne, should he direcion of he magneic force poin up or down? Predicion 3-4: Suppose you move he loop from well below he magne o well above flow when he loop is above he magne, should he direcion of he magneic force poin up or down? TESTIN THE PREDICTIONS Firs, ake off your wriswach. Second, connec he leads o he coil, forming a closed loop (you can use a clip from he Curren Sensor leads for his, bu ake he Curren Sensor ou of he circui). Move he coil up and down over he magne. Can you deec any magneic force? Try moving he coil more quickly. However, he quicker you move he coil, he more force you have o apply o he coil, and he harder i migh be o deec he magneic force. Quesion 3 (answer on your ear-off shee a he end): Were you able o verify your predicions? To obain a more easily deeced magneic force, we need induced currens ha are larger han hose which can be produced in he coil. The aluminum sleeve ha is par of he apparaus is conducing bu non-magneic. Verify he non-magneic propery of aluminum par by holding he sleeve near he magne and noing he absence of aracion. Now, ry moving he sleeve up and down on he Plexiglas ube pas he magne, and verify your predicions and summary above. Feel he Ids B ex force! Hold he sleeve a he op of he plasic column, and le i drop. When you le he sleeve drop, he magneic force opposed graviy (he exernal force). E09-5
Par 4: The Srucure of Space and Time Einsein sars his 1905 paper on special relaiviy wih he following paragraph (see On The Elecrodynamics of Moving Bodies by A. Einsein) I is known ha Maxwell's elecrodynamics--as usually undersood a he presen ime-- when applied o moving bodies, leads o asymmeries which do no appear o be inheren in he phenomena. Take, for example, he reciprocal elecrodynamic acion of a magne and a conducor. The observable phenomenon here depends only on he relaive moion of he conducor and he magne, whereas he cusomary view draws a sharp disincion beween he wo cases in which eiher he one or he oher of hese bodies is in moion. For if he magne is in moion and he conducor a res, here arises in he neighborhood of he magne an elecric field wih a cerain definie energy, producing a curren a he places where pars of he conducor are siuaed. Bu if he magne is saionary and he conducor in moion, no elecric field arises in he neighborhood of he magne. In he conducor, however, we find an elecromoive force, o which in iself here is no corresponding energy, bu which gives rise--assuming equaliy of relaive moion in he wo cases discussed--o elecric currens of he same pah and inensiy as hose produced by he elecric forces in he former case. Wha he is saying is ha i doesn make any difference in he curren you observe as o wheher he magne is saionary and he coil moves or he coil is saionary and he magne moves. Check o see ha his is correc. Tha is, hold he coil saionary and move he magne hrough i, and see if you observe he same curren signaure as in he above experimens. Chose one: Curren depends on relaive velociy of coil and magne only (Einsein righ) Curren depends on wheher he magne is a res and he coil moves or vice versa (Einsein wrong) In he las class before he exam review, we will show you why his observaion led Einsein o deduce he naure of space and ime i.e., space conracion, ime dilaion, and all hose oher weird hings. I all grew ou of classical elecromagneism. E09-6
MASSACHUSETTS INSTITUTE OF TECHNOLOY Deparmen of Physics 8.02 Spring 2005 Tear off his page and urn i in a he end of class. Noe: Wriing in he name of a suden who is no presen is a Commiee on Discipline offense. Experimen Summary 9: Faraday s Law of Inducion roup and Secion (e.g. 10A, L02: Please Fill Ou) Names Par 1: Predicions of Magneic Flux and Induced Curren The curves from which you choose are reproduced here: (1) (2) (3) (4) Predicion 1-1: Suppose you move he loop from well above he magne o well below he magne a a consan speed. The graph of he magneic flux hrough he loop as a funcion of ime would mos closely resemble: Curve Predicion 1-2: Suppose you move he loop from well above he magne o well below he magne a consan speed. The graph of he curren as a funcion of ime would mos closely resemble Curve. E09-7
Predicion 1-3: Suppose you move he loop from well below he magne o well above he magne a a consan speed. The graph of he magneic flux hrough he loop as a funcion of ime would mos closely resemble: Curve Predicion 1-4: Suppose you move he loop from well below he magne o well above he magne a consan speed. The graph of he curren versus ime would mos closely resemble: Curve. Par 2: Measuremens of Induced Curren and Flux Quesion 1: Did your predicions agree wih your measuremens? Quesion 2: Noe ha no maer how fas or slow you move he coil up and down pas he magne, as long as you go from far above o far below, or from far below o far above, he flux funcion will always aain he same maximum value in he process. Why? Par 3: Feel he ( Ids B ) Force! Predicion 3-1: Suppose you move he loop from well above he magne o well below flow when he loop is above he magne, should he direcion of he magneic force poin up or down? up down Predicion 3-2: Suppose you move he loop from well above he magne o well below flow when he loop is below he magne, should he direcion of he magneic force poin up or down? up down Predicion 3-3: Suppose you move he loop from well below he magne o well above flow when he loop is below he magne, should he direcion of he magneic force poin up or down? up down Predicion 3-4: Suppose you move he loop from well below he magne o well above flow when he loop is above he magne, should he direcion of he magneic force poin up or down? up down Quesion 3: Were you able o verify your predicions? Par 4: The Srucure of Space and Time Curren depends on relaive velociy of coil and magne only (Einsein righ) Curren depends on wheher he magne is a res and he coil moves or vice versa (Einsein wrong) E09-8