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Maxwell’s Equations and Electromagnetic Waves

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Setting the Stage - The Displacement Current Maxwell had a crucial “leap of insight”... Will there still be a magnetic field around the capacitor?

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A Beautiful Symmetry... A changing magnetic flux produces an Electric field A changing electric flux produces a Magnetic field

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An extension of Ampere’s Law... Maxwell reasoned that Ampere’s Law would also apply to the displacement current. Clever application of Gauss’ Law here!

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Maxwell’s Equations (first glimpse) Faraday’s Law: Ampere’s Law:

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Maxwell’s Equations – Integral Form Faraday’s Law: Ampere’s Law: Gauss’ Law

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Maxwell’s Equations – Differential Form Gauss’ Theorem – integral of a flux equals volume integral of divergence

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Maxwell’s Equations – Differential Form Stoke’s Theorem: “Integral around the path equals flux of the curl”

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Maxwell’s Equations – Differential Form

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The Wave Equation How fast will a wave travel along a string of density ?

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Two Ways to M’Es… Abstract: Physical: –Imagine a plane wave of electric field in z- direction

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Go to Rob Salgado’s sim of this

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Moving Fields… Moving E-Field leads to… Moving B-Field leads to…

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It’s Alive! Well, at least it’s a wave! Combining the last two equations leads us to: example - consider the electric field part of an electromagnetic wave described by:

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The Poynting Vector Light waves (and all electromagnetic waves) carry energy A wave has an intensity Poynting Vector

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Radiation Pressure Light waves (and all electromagnetic waves) exert pressure

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Accelerating Charges Radiate Power! We can show (by dimensional argument) that an accelerating charge should radiate energy at a rate given by: More detailed argumentation reveals that = 2/3

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Chapter 32 Maxwell’s Equations Electromagnetic Waves.

Chapter 32 Maxwell’s Equations Electromagnetic Waves.

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