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Winter wk 9 – Mon.28.Feb.05 Energy Systems, EJZ

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Maxwell Equations in vacuum Faraday: Electric fields circulate around changing B fields Ampere: Magnetic fields circulate around changing E fields

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Faraday’s law in differential form

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Ampere’s law in differential form

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Maxwell’s eqns for postulated EM wave

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Do wave solutions fit these equations? Consider waves traveling in the x direction with frequency f= and wavelength = /k E(x,t)=E 0 sin (kx- t) and B(x,t)=B 0 sin (kx- t) Do these solve Faraday and Ampere’s laws? Under what condition?

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Differentiate E and B for Faraday Sub in: E=E 0 sin (kx- t) and B=B 0 sin (kx- t)

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Differentiate E and B for Ampere Sub in: E=E 0 sin (kx- t) and B=B 0 sin (kx- t)

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Maxwell’s eqns in algebraic form Subbed in E=E 0 sin (kx- t) and B=B 0 sin (kx- t) Recall that speed v = /k. Solve each equation for B 0 /E 0

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Speed of Maxwellian waves? Ampere B 0 /E 0 = 0 v Faraday B 0 /E 0 = 1/v Eliminate B 0 /E 0 and solve for v: 0 = x m = x C 2 N/m 2

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Maxwell equations Light

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Energy of EM waves Electromagnetic waves in vacuum have speed c and energy/volume = E and B vectors point (are polarized) perpendicular to the direction the wave travels. EM energy travels in the direction of the EM wave. Poynting vector =

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