Chapter 20Michael FaradayFaraday’s Experiment – Set UpFaraday’s ExperimentFaraday’s ConclusionsMagnetic FluxMagnetic Flux, 2Magnetic Flux, 3Magnetic Flux, finalElectromagnetic Induction – An ExperimentElectromagnetic Induction – Results of the ExperimentFaraday’s Law and Electromagnetic InductionFaraday’s Law and Lenz’ LawLenz’ Law – ExampleApplications of Faraday’s Law – Ground Fault InterruptersApplications of Faraday’s Law – Electric GuitarApplications of Faraday’s Law – Apnea MonitorApplication of Faraday’s Law – Motional emfMotional emfMotional emf, contMotional emf in a CircuitMotional emf in a Circuit, contLenz’ Law Revisited – Moving Bar ExampleLenz’ Law, Bar Example, contLenz’ Law, Bar Example, finalLenz’ Law Revisited, Conservation of EnergyLenz’ Law – Moving Magnet ExampleLenz’ Law, Final NoteApplication – Tape RecorderGeneratorsAC Generators, contAC Generators, finalAC Generators – Detail of Rotating LoopDC GeneratorsDC Generators, contMotorsMotors and Back emfMotors and Back emf, contSelf-inductanceSelf-inductance contSelf-inductance, finalJoseph HenryInductor in a CircuitRL CircuitRL Circuit, contEnergy Stored in a Magnetic FieldChapter 20Induced Voltages and InductanceMichael Faraday1791 – 1867Great experimental scientistInvented electric motor, generator and transformersDiscovered electromagnetic inductionDiscovered laws of electrolysisFaraday’s Experiment – Set UpA current can be produced by a changing magnetic fieldFirst shown in an experiment by Michael FaradayA primary coil is connected to a batteryA secondary coil is connected to an ammeterFaraday’s ExperimentThe purpose of the secondary circuit is to detect current that might be produced by the magnetic fieldWhen the switch is closed, the ammeter reads a current and then returns to zeroWhen the switch is opened, the ammeter reads a current in the opposite direction and then returns to zeroWhen there is a steady current in the primary circuit, the ammeter reads zeroFaraday’s ConclusionsAn electrical current is produced by a changing magnetic fieldThe secondary circuit acts as if a source of emf were connected to it for a short timeIt is customary to say that an induced emf is produced in the secondary circuit by the changing magnetic fieldMagnetic FluxThe emf is actually induced by a change in the quantity called the magnetic flux rather than simply by a change in the magnetic fieldMagnetic flux is defined in a manner similar to that of electrical fluxMagnetic flux is proportional to both the strength of the magnetic field passing through the plane of a loop of wire and the area of the loopMagnetic Flux, 2You are given a loop of wireThe wire is in a uniform magnetic field The loop has an area AThe flux is defined asΦB = BA = B A cos θθ is the angle between B and the normal to the planeBrMagnetic Flux, 3When the field is perpendicular to the plane of the loop, as in a, θ = 0 and ΦB = ΦB, max = BAWhen the field is parallel to the plane of the loop, as in b, θ = 90° and ΦB = 0The flux can be negative, for example if θ = 180°SI units of flux are T. m² = Wb (Weber)Magnetic Flux, finalThe flux can be visualized with respect to magnetic field linesThe value of the magnetic flux is proportional to the total number of lines passing through the loopWhen the area is perpendicular to the lines, the maximum number of lines pass through the area and the flux is a maximumWhen the area is parallel to the lines, no lines pass through the area and the flux is 0Electromagnetic Induction –An ExperimentWhen a magnet moves toward a loop of wire, the ammeter shows the presence of a current (a)When the magnet is held stationary, there is no current (b)When the magnet moves away from the loop, the ammeter shows a current in the opposite direction (c)If the loop is moved instead of the magnet, a current is also detectedElectromagnetic Induction – Results of the ExperimentA current is set up in the circuit as long as there is relative motion between the magnet and the loopThe same experimental results are found whether the loop moves or the magnet movesThe current is called an induced current because is it produced by an induced emfFaraday’s Law and Electromagnetic InductionThe instantaneous emf induced in a circuit equals the time rate of change of magnetic flux through the circuitIf a circuit contains N tightly wound loops and the flux changes by ΔΦB during a time interval Δt, the average emf induced is given by Faraday’s Law:tNBFaraday’s Law and Lenz’ LawThe change in the flux, ΔΦB, can be produced by a change in B, A or θSince ΦB = B A cos θThe negative sign in Faraday’s Law is included to indicate the polarity of the induced emf, which is found by Lenz’ Law The current caused by the induced emf travels in the direction that creates a magnetic field with flux opposing the change in the original flux through the circuitLenz’ Law – ExampleThe magnetic field, , becomes smaller with timeThis reduces the fluxThe induced current will produce an induced field, ind, in the same direction as the original fieldBrBrBrApplications of Faraday’s Law – Ground Fault InterruptersThe ground fault interrupter (GFI) is a safety device that protects against electrical shockWire 1 leads from the wall outlet to the applianceWire 2 leads from the appliance back to the wall outletThe iron ring confines the magnetic field, which is generally 0If a leakage occurs, the field is no longer 0 and the induced voltage triggers a circuit breaker shutting off the currentApplications of Faraday’s Law – Electric GuitarA vibrating string induces an emf in a coilA permanent magnet inside the coil magnetizes a portion of the string nearest the coilAs the string vibrates at some frequency, its magnetized segment produces a changing flux through the pickup coilThe changing flux produces an induced emf that is fed to an amplifierApplications of Faraday’s Law – Apnea MonitorThe coil of wire attached to the chest carries an alternating currentAn induced emf produced by the varying field passes through a pick up coilWhen breathing stops, the pattern of induced voltages stabilizes and external monitors sound an alertApplication of Faraday’s Law –