Lecture_26

# Lecture_26 - Maxwell's Equations Four equations(integral...

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Four equations (integral form) : Gauss’s law Gauss’s law for magnetism Faraday’s law Ampere-Maxwell law ! " = # 0 ˆ \$ inside q dA n E ! ! B ! ˆ ndA " " = 0 [ ] ! ! " # = " dA n B dt d l d E ˆ ! ! ! ! " # \$ % + = ( ) * dt d I l d B elec path inside 0 _ 0 + μ ! ! + Lorentz force B v q E q F ! ! ! ! ! + = Maxwell’s Equations

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Time varying magnetic field makes electric field Time varying electric field makes magnetic field Do we need any charges around to sustain the fields? Is it possible to create such a time varying field configuration which is consistent with Maxwell’s equation? Solution plan: • Propose particular configuration • Check if it is consistent with Maxwell’s eqs • Show the way to produce such field • Identify the effects such field will have on matter • Analyze phenomena involving such fields Fields Without Charges
vE B 0 0 ! μ = E=Bv vBv B 0 0 = 2 0 0 1 v = m/s 8 0 0 10 3 1 ! = = " v Based on Maxwell’s equations, pulse must propagate at speed of light A Pulse: Speed of Propagation Faraday’s law Ampere’s law E=cB

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by vector product B E ! ! ! Direction of Propagation
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Lecture_26 - Maxwell's Equations Four equations(integral...

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