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-Generators -Motors -Eddy Currents -Maxwell’s Four Equations AP Physics C Mrs. Coyle

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Applet Link: http://www.walter- fendt.de/ph14e/generator_e.htm Electric generators convert mechanical energy to electrical energy AC Generators Do not have a commutator DC Generators Have a commutator

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AC Generator

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Rotating Loop in a Generator Loop has N turns The flux through the loop at any time t : B = BA cos B =BA cos t

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Induced emf in a Rotating Loop max = NAB

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Induced emf in a Rotating Loop max occurs when t = 90 o or 270 o –This occurs when the magnetic field is in the plane of the coil and the time rate of change of flux is a maximum = 0 when t = 0 o or 180 o –This occurs when B is perpendicular to the plane of the coil and the time rate of change of flux is zero

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DC Generators The DC (direct current) generator has essentially the same components as the AC generator The main difference is that the contacts to the rotating loop are made using a split ring called a commutator

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DC Generators In this configuration, the output voltage always has the same polarity and pulsates with time To obtain a steady DC current, commercial generators use many coils and commutators distributed so the pulses are out of phase

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Motors A motor is a generator operating in reverse Electrical energy is converted to mechanical energy A current is supplied to the coil by a battery and the torque acting on the current-carrying coil causes it to rotate

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Back emf of a Motor As the coil rotates in a magnetic field, an emf is induced in the coil –This induced emf always acts to reduce the current in the coil and is called back emf –The back emf increases in magnitude as the rotational speed of the coil increases

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The power requirements for starting a motor and for running it are greater for heavy loads than for light ones

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Voltage Transformers

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Current Transformers

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Eddy Currents Circulating currents that are induced in bulk pieces of metal moving through a magnetic field The eddy currents are in opposite directions as the plate enters or leaves the field Are often undesirable because they represent a transformation of mechanical energy into internal energy

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Maxwell’s Equations

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Gauss’s law (electrical): The total electric flux, Φ E =, through any closed surface equals the net charge inside that surface divided by o This relates an electric field to the charge distribution that creates it

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Gauss’s law (magnetism): The total magnetic flux through any closed surface is zero The number of field lines that enter a closed volume must equal the number that leave that volume The magnetic field lines cannot begin or end at any point Isolated magnetic monopoles have not been observed in nature

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Faraday’s law of Induction: An electric field is created by a changing magnetic flux Induced voltage Emf=- around any closed path, equals the rate of change of the magnetic flux through any surface bounded by that path Example: A current is induced in a conducting loop placed in a time-varying B

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Ampere-Maxwell Law A generalization of Ampere’s law Creation of a magnetic field by a changing electric field and electric currents The line integral of the magnetic field around any closed path is the given sum

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The Lorentz Force Law F = qE + qv x B Maxwell’s equations, together with this force law, completely describe all classical electromagnetic interactions

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Induced Voltages and Inductance

Induced Voltages and Inductance

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