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Published byHillary Wheeler Modified over 8 years ago
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Faraday’s Law M&I Chapter 23
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Maxwell’s Equations (so far…) *Not complete
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for fields made by charges at rest. Can a distribution of static charges make this field? Electrostatic forces are conservative. The change in potential around a loop must be zero.
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means: No curly electric fields. BUT: This is only true for “Coulomb” fields (fields caused by stationary charges).
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There is another way to make electric fields.
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Solenoid
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Curly electric field (both inside and outside solenoid)
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Where there is a time-varying magnetic field, there is also a curly electric field.
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No curly electric field
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We call the curly electric fields Non-Coulomb electric fields E NC They are related to magnetic fields that are changing in time:
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Which direction does the electric field curl?
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Right thumb along Fingers curl in direction of
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Which direction does the electric field curl?
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What if we put a conducting wire around the solenoid? A current is induced in the wire.
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Solenoid B increasing Metal wire How big is the current I 2 ?
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EMF (ElectroMotive Force) EMF is actually not a force. It is the energy per unit charge added to a circuit during a single round trip. EMF = Units: Volts
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Metal wire EMF = Solenoid B increasing
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Metal wire (Ohm’s Law) 电阻 Solenoid B increasing
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We can measure E NC by measuring the induced current.
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Experiments: I 2 is only present when I 1 is changing. EMF
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Experiments: i 2 is proportional to the area of the solenoid. EMF
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Faraday’s Law This is the magnetic flux through the loop. EMF
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Faraday’s Law The EMF around a closed path is equal to the rate of change of the magnetic flux inside the path. EMF
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Faraday’s Law The EMF around a closed path is equal to the rate of change of the magnetic flux inside the path.
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Michael Faraday (1791 – 1876)
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Solenoid Wire Ammeter 电表 The magnetic field in the solenoid increases from 0.1 T to 0.7 T in 0.2 seconds. What current will the ammeter measure? Example
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Solenoid Wire Ammeter 电表 The magnetic field in the solenoid increases from 0.1 T to 0.7 T in 0.2 seconds. What current will the ammeter measure? Example
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EMF in a coil with many turns B increasing
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EMF in a coil with many turns B increasing
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EMF in a coil with many turns B increasing
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Solenoid Wire Ammeter 电表 The ammeter measures a current of 10 A. Now, we replace the single wire with a coil containing N = 20 turns. What is the current now? Example
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Maxwell’s Equations (so far…) *Not complete
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Maxwell’s Equations (so far…) *Not complete Gauss’ Law for electric fields Gauss’ Law for magnetic fields Faraday’s Law
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Maxwell’s Equations (so far…) Gauss’ Law for electric fields Gauss’ Law for magnetic fields Faraday’s Law Ampere-Maxwell Law
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Maxwell’s equations predict travelling waves.
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Maxwell’s equations predict light.
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