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**AP Physics C Montwood High School R. Casao**

Maxwell’s Equations AP Physics C Montwood High School R. Casao

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Four equations, known as Maxwell’s equations, are regarded as the basis of all electrical and magnetic phenomena. These equations are as fundamental to electromagnetic phenomena as Newton’s laws are to mechanical phenomena. The theory developed by Maxwell turned out to be in agreement with Einstein’s theory of relativity. The equations predicted the existence of electromagnetic waves (traveling patterns of electric and magnetic fields), which travel at a speed of

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Time Sequence of E and B

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**The theory also showed that electromagnetic waves are radiated by accelerating charges.**

Maxwell’s equations (in free space):

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Gauss’ law states that the total electric flux thru any closed surface equals the net charge inside that surface divided by εo. The law relates the electric field to the charge distribution, where electric field lines originate on positive charges and terminate on negative charges. Gauss’s law in magnetism says that the net magnetic flux thru a closed surface is zero. The number of magnetic field lines that enter a closed volume must equal the number of magnetic field lines that leave that volume. Magnetic field lines cannot begin or end at any point. If they did, isolated magnetic monopoles would exist at those points. Magnetic monopoles have never been observed.

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Faraday’s law of induction describes the relationship between an electric field and a changing magnetic flux. The line integral of the electric field around any closed path (which equals the EMF) equals the rate of change of magnetic flux thru any surface area bounded by that path. Ampere-Maxwell’s equation describes the relationship between magnetic and electric fields and electric currents. The line integral of the magnetic field around any closed path is determined by the sum of the net conduction current thru that path and the rate of change of electric flux thru any surface bounded by that path.

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Once the electric and magnetic fields are known at some point in space, the force on a particle of charge q can be calculated from the expression: The force is called the Lorentz force.

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