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Chapter 22 Electromagnetic Induction

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1) Induced emf and induced current Changing B-field induces current

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Changing coil area or orientation induces current

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Changing the number of lines of force through loop induces current Induced current indicates induced emf and induced electric field Changing magnetic field produces electric field

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2) Motional emf a)The principle B-field exerts force on moving charges + v FBFB - v FBFB

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==> free charges separate E E separated charges produce electric field and a corresponding potential difference

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E E E - field exerts force on charges + FEFE - FEFE

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E E Charges stop moving when the forces balance: Induced emf predicted from statics so,

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b) Application

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c) Induced emf from conservation of energy F A = F B FBFB

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FBFB Power to push rod at speed v: Using,

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F A = F B FBFB Power to push rod at speed v: Electrical power consumed: So,

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3) Magnetic flux, a)Define Flux: - Proportional to the lines of force through a surface

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Flux depends on angle

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b) Flux and motional emf t

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4) Lenz’s law Direction of induced current produces a magnetic field that opposes the change in flux -flux through loop (in) increases because of v: t > 0 - induced current produces flux out of diagram (opposite direction) -Define flux from external field as positive. Then

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-flux through loop (in) decreases because of v: t < 0 - induced current produces flux into loop (same direction to oppose the decrease) -Define external flux as positive. Then induced flux is also positive, so again v

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5) Faraday’s Law For any changing flux in any loop, the emf induced in the loop is (for N turns) where is the flux through one turn

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a) Conservation of energy Lenz’s law is statement of energy conservation Flux increases Induced field repels magnet; work required to produce current

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Flux decreases Induced field attracts magnet; work required to produce current

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Example: Find direction of the current in each loop zero ccw cw

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b) Induced polarity Inside the loop, current is forced from negative to positive (by work that produces the change in flux) I (like inside a battery) In the external circuit, current flows from positive to negative

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c) Eddy currents Power loss hence, laminated cores in transformers

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Induction stove

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6) Electric Generator

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a) The principle

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b) Conservation of energy and countertorque If I = 0, coil turns without resistance If I > 0, force on wires resists spinning Larger load requires more fuel

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c) Back emf of an electric motor Rotating coil in a motor acts like a generator According to Lenz’s law, the induced emf opposes external current more power required initially to accelerate motor higher speed produces higher back emf, and lower current max speed --> minimum current (minimum power) stopped motor draws maximum current

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7) Induction and sound Microphone

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Guitar pickup

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Magnetic tape

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