Chapter 10 - Time Varying Fields and Maxwell's Equations

# Chapter 10 - Time Varying Fields and Maxwell's Equations -...

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Time Varying Fields and Maxwell’s Equations Chapter 10

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Time Time ’s Equations s Equations Time-varying magnetic fields Time-varying electric fields Electric field produced by time-varying magnetic field - Michael Faraday Magnetic Field produced by time-varying electric field -James Clerk Maxwell
Chapter 10 Time Time ’s Equations s Equations Faraday’s Law A time-varying magnetic field produces an electromotive force (emf) which may establish a current in a suitable closed circuit. What is emf? A voltage that arises from conductors moving in a magnetic field or from changing magnetic fields.

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Φ : flux through a closed path The minus sign indicates that the emf is in a direction as to produce a current whose flux, if added to the original flux, would reduce the magnitude emf. OR The minus sign indicates that the emf is in a direction as to produce a current whose flux would oppose the changing flux volts dt d emf Φ - =
Illustration: increasing magnetic field direction of induced current _ + polarity of induced emf

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Lenz’s Law Induced voltage acts to produce an opposing flux. For an N-turn conductor coil: About a specific closed path Note: In electrostatics, dt d N emf Φ - = L d E emf = 0 L E = d Recall:
Let : the time rate of change of flux - = Φ = = s d dt d d emf S B dt d - L E dt d Φ = Φ s d S B

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A time changing flux is linking a stationary closed path
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## This note was uploaded on 01/13/2011 for the course EEEI 23 taught by Professor Joeljosephmarciano during the Winter '10 term at University of the Philippines Diliman.

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Chapter 10 - Time Varying Fields and Maxwell's Equations -...

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