Physics for Scientists and Engineers 8ed - ch34 - PowerPoint Slides

Physics for Scientists and Engineers 8ed - ch34 - PowerPoint Slides

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Chapter 34 Electromagnetic Waves
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James Clerk Maxwell 1831 – 1879 Scottish physicist Provided a mathematical theory that showed a close relationship between all electric and magnetic phenomena His equations predict the existence of electromagnetic waves that propagate through space Also developed and explained Kinetic theory of gases Nature of Saturn’s rings Color vision
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Modifications to Ampère’s Law Ampère’s Law is used to analyze magnetic fields created by currents: But this form is valid only if any electric fields present are constant in time Maxwell modified the equation to include time-varying electric fields Maxwell’s modification was to add a term o d d I = Β σ r r g μ
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Modifications to Ampère’s Law, cont The additional term included a factor called the displacement current , I d This term was then added to Ampère’s Law Now sometimes called Ampère-Maxwell Law This showed that magnetic fields are produced both by conduction currents and by time-varying electric fields E d o d I d dt Φ =
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Maxwell’s Equations In his unified theory of electromagnetism, Maxwell showed that electromagnetic waves are a natural consequence of the fundamental laws expressed in these four equations: 0 o B E o o o q d d d d d d d d I d d dt dt = = Φ Φ = - = + Ε Α Β Α Ε σ Β σ r r r r r r r r r r r r
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Maxwell’s Equation 1 – Gauss’ Law The total electric flux through any closed surface equals the net charge inside that surface divided by ε o This relates an electric field to the charge distribution that creates it o q d d = Ε Α r r r
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Maxwell’s Equation 2 – Gauss’ Law in Magnetism The net magnetic flux through a closed surface is zero The number of magnetic field lines that enter a closed volume must equal the number that leave that volume If this wasn’t true, there would be magnetic monopoles found in nature There haven’t been any found 0 d = Β Α r r r
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Maxwell’s Equation 3 – Faraday’s Law of Induction Describes the creation of an electric field by a time- varying magnetic field The emf, which is the line integral of the electric field around any closed path, equals the rate of change of the magnetic flux through any surface bounded by that path One consequence is the current induced in a conducting loop placed in a time-varying magnetic field B d d dt Φ = - Ε σ r r r
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Maxwell’s Equation 4 – Ampère-Maxwell Law Describes the creation of a magnetic field by a changing electric field and by electric current The line integral of the magnetic field around any closed path is the sum of μ o times the net current through that path and ε ο μ o times the rate of change of electric flux through any surface bounded by that path E o o o d d d I d d dt Φ = + Β σ r r r
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Lorentz Force Law Once the electric and magnetic fields are known at some point in space, the force
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Physics for Scientists and Engineers 8ed - ch34 - PowerPoint Slides

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