Maxwell Equations & EM Waves
Physics 4B
M. Rocha
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Gasuss's Law
Gauss law for magnetism
Maxwell-Faraday equation (Faraday induction law)
Ampere’s Law (with the addition of Maxwell)
You already know most of Maxwell's Equations!
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You already know most of Maxwell's Equations!
Gauss's Law for Magnetism
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Magnetic Poles
North Pole: Side where field lines point away from the source
South Pole: Side where field lines point into the source
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Not known magnetic Monopoles
Unlike electric charges, cannot have just a North or just a South magnetic pole
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Maxwell-Faraday Equation (Induction Law)
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Induced Electric Fields
- The induced emf due to changing magnetic fields is the result of the electric field doing work on the moving charges
- The work done by 𝐄⃗ in moving a unit charge completely around a circuit is the induced emf ε
- Faraday’s law can be written in terms of the induced electric field as
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Maxwell-Ampere's Law
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Maxwell's Addition To Ampere's Law
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Ampere's Law
Maxwell suggested adding the displacement current
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Gasuss's Law
Gauss law for magnetism
Maxwell-Faraday equation (Faraday induction law)
Ampere’s Law (with the addition of Maxwell)
Maxwell’s equations and the Lorentz force law together encompass all the laws of electricity and magnetism.
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Lorentz force law
Electro-Magnetic Waves
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In free space (no currents or charges), Maxwell's equations reduce to
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The speed of light
From maxwells equations in free space you can derive two symmetric wave equations (link to derivation)
Energy and Momentum of EM Waves
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The time average of the energy flux is the intensity I of the electromagnetic wave and is the power per unit area.
where E0 and B0 are the maximum strengths/amplitude of the E and B fields and
The momentum can be found in terms of the Intensity of the EM wave, and is given by
The End
Maxwell Equations & EM Waves
By Miguel Rocha
Maxwell Equations & EM Waves
- 542