FARADAY S LAW OF INDUCTION (Chapter 23)

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Lawrence Phelps
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1 FAADAY S LAW OF NDUCTON (Chapter 23) Look at a conductor moing ACOSS magnetic field lines Free electrons moe perpendicular to (into page) o Electrons (neg.) feel force F e Force on electrons is down F in o esult is potential difference induced between ends of bar bottom more negatie CONCLUSON: potential difference can be induced across a conductor moing through a magnetic field Will come back to this example later when we hae more theory

2 SOME DEMONSTATONS: A magnet moing into/out of a loop of wire induces a current o See fig in text Ammeter N S Starting/stopping current through loop in one coil (primary) causes pulse of current in coil (secondary) linked by iron coil - this is a transformer o See fig in text switch battery primary iron secondary Ammeter FAADAY S CONCLUSON from obserations like these: Time-arying magnetic fields can induce currents To quantify, need to relate induced potential difference to changing magnetic flux

3 MAGNETC FLUX: proportional to number of magnetic field lines through area area element da : ector perpendicular to area element contribution to magnetic flux from da is Total flux through area is da area Unit for flux is Tm 2 Wb (1 Weber) da da emf symbol is Work to push unit charge through a wire (or space) Units of emf are olts attery is source of emf originally electromotie force UT not a force: long name no longer used f resistance in loop is, then current in loop is /

4 FAADAY S LAW OF NDUCTON Look at circuit bounding a surface of area A f magnetic flux through surface changes with time: o induces emf around circuit Faraday s Law of induction relates emf to rate of change of flux: d will think about meaning of minus sign later if circuit is coil of N turns: N d

5 Sources of time-arying magnetic flux t look at loop of area A in field with angle between and normal A o magnetic flux is: A Acos A SO Faraday s law is d Acos Can induce emf by: arying magnitude arying magnitude A arying angle (i.e. rotating coil as in a generator) combination of aboe

6 EXAMPLE (see Exs. 23.1, 23.2) : A loop of wire is located in a uniform magnetic field that is changing with time. What is the induced emf? is uniform oer the surface of area A bounded by the loop of wire so: A Acos A o A and θ are constant. o depends on time So: d Acos

7 emf NDUCED Y MOTON OF CONDUCTO THOUGH MAG. FELD (23.2) 1 st : Look at straight conductor: Conductor to ; to ; to length of conductor Magnetic force on free electrons in conductor is: F e e (down) o lower end more negatie; upper end more positie F in electrons moe UNTL resulting electric and magnetic forces balance o alances when FE F so that ee e o Magnitude of potential difference between conductor ends: V El l F E As long as is constant Top of conductor is positie (here) F in

8 2 nd : Complete circuit: ar sliding on conducting rails connected by resistance Pull bar to right with force F APP Can get direction of from picture in preious section l F What is magnitude of? in Use Faraday s Law: Magnetic flux through area bounded by circuit is x l x nduced emf is d l d x l Magnitude of current is l

9 Sliding ar: Power dissipated (as heat) in resistance is Where does this energy come from? P 2 Look at force needed to pull bar to right at constant speed? Current flows up in bar causes magnetic force on bar : F l l (left) For constant speed, net force is zero. So applied force is: F l (right) APP l x F F APP in Power deliered by applied force is P F APP l ut from can write l So Power deliered by applied force is P l l l Same as power dissipated in resistor CONSEVATON OF ENEGY 2

10 EXAMPLE: emf nduced in a otating ar A bar of length l is rotating in a plane perpendicular to magnetic field with angular speed. What is the emf induced across the length of the bar? r l ω

11 Alternating Current Generator: A loop rotating about an axis to Flux through loop depends on angle between and loop normal ector o A Acos N S f loop is rotating with angular speed, then t o Then t Acos t t f there are N turns in the loop then induced emf is N S o d N esult is AC oltage: o Amplitude is dcos t NA NA sin t max NA sin t NA ε max ε t

12 Alternating Current Generator (continued): nduced emf is NA sin t nduced emf 0 when t t 0 o i.e. when loop normal is parallel to N A S o at this orientation, edges of loop are not cutting any field lines nduced emf max NA when t t / 2 o i.e. when loop normal is perpendicular to N A S o at this orientation, edges of loop are cutting field lines For real AC generator, need slip rings to connect to rotating coil o AC is OK for heat, lights, etc. To get DC oltage, need a rectifier

13 LENZ S LAW: gies direction of induced current when flux through loop changes ule for polarity of induced emf in loop: o esulting current will be in direction that tends to produce a magnetic field that opposes the change in flux that induced the emf Example: ar moing to right increases magnetic flux through loop o Lenz s law resulting current should cause field tending to cancel increased flux in loop in o SO: from induced current should be out. Means that induced current should be ccw o Will generate out of page/screen NSDE the loop (by H-rule) in induced

14 EXAMPLE: Moe bar magnet right toward loop o ncreases flux through loop y Lenz s Law, current induced in loop should oppose increase in flux through loop o Means that induced current should generate field pointing to left S N esult: Current in loop generates magnetic dipole pointing to left induced o Acts like magnet with north pole to left induced DEMONSTATONS: Magnetic leitation (jumping rings) Eddy current pendulum

Induced voltages and Inductance Faraday s Law

Induced voltages and Inductance Faraday s Law concept #1, 4, 5, 8, 13 Problem # 1, 3, 4, 5, 6, 9, 10, 13, 15, 24, 23, 25, 31, 32a, 34, 37, 41, 43, 51, 61 Last chapter we saw that a current produces a magnetic