Lecture 9 Electromagnetic InductionElectromagnetic InductionMagnetic FluxFaraday’s Law of InductionPolarity of the Induced EmfMotional EmfSummaryLecture 9Electromagnetic InductionChapter 20.1 20.4Outline•Induced Emf•Magnetic Flux•Faraday’s Law of InductionElectromagnetic InductionIf an electric current produces a magnetic field, then a magnet should be able to generate an electric current.A current is produced in a wire when there is relative motion between the wire and a magnetic field.Such a current is called an induced current (emf).The effect is called electromagnetic induction (discovered by Michael Faraday in the XIX century).The strength of the current depends on the magnetic field strength and the wire’s speed.Magnetic FluxThe emf is induced by the magnetic flux, rather than the magnetic field.Magnetic flux is a measure of the total number of magnetic lines passing through an area.Consider a loop of wire in the presence of a uniform magnetic field B. If the loop area is A, then the magnetic flux B through it is defined as:B = BA = BA cos B is the component of B, perpendicular to the plane of the loopFaraday’s Law of InductionThe induced emf exists only when there is a relative motion between the magnet and the circuit.Faraday’s law states that the instantaneous induced emf equals the rate of change of magnetic flux through the circuit.If a circuit has N loops and the flux through each loop changes by the amount of B during interval of time t, the average emf ℇ induced in the circuit during this time is:ℇ = N B/tPolarity of the Induced EmfThe induced emf produces an induced current.The induced current produces its own magnetic field.The induced magnetic field opposes the change of the external magnetic field.The polarity (direction) of the induced emf is determined by Lenz’s law.Motional EmfLet us consider an application of Faraday’s law to a conductor of length l moving at a constant velocity v through a uniform magnetic field.PictureF = qvBqE = qvBE = vB Magnetic force on electrons in the conductorE is the electric field induced in the conductorE is uniform the potential difference across the conductor ends V = E lSummary•The phenomenon of electromagnetic induction refers to appearance of an electric field under influence of a magnetic field.•Faraday’s law connects the induced emf and time change in the magnetic flux.•Lenz’s law defines the polarity of the induced emf•Motional emf is an emf produced in a moving conductor under influence of a magnetic
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