Lec11 - is a B field is increasing so that there is a...

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Unformatted text preview: is a B field is increasing, so that there is a time–changing B –field flux through the loop. The E field between the wavefront and the current sheet is parallel to the current sheet, and counter-parallel to the current. (This is easy to see given the propagation direction of the electromagnetic wave and the direction of B .) That is, E = E ˆ y . (See Fig. 6.) Using the Faraday law, ∂A E · d S =- d Φ B dt , one finds that the RHS equals ∂A E · d S =- E Δ y , and the flux of the B field through the loop at the time t > t is Φ B = B c ( t- t ) Δ y , so that the RHS of the Faraday law equals- d Φ B / dt =- cB Δ y . Setting the two hand sides equal, we find E Δ y = cB Δ y , or E = cB . Although our argument was made only for the configuration of a current sheet that is abruptly turned on, the result that E = cB for an electromagnetic wave is general. The general result, however, is beyond the scope of the introductory course. An important con- sequence is that in an electromagnetic wave the E and B fields are in phase . That is, as at any given time E = cB , when E is maximal so is B , when E vanishes B is zero too, etc. The result that E = cB appears in many introductory texts. However, in such books an extra assumption is typically made, namely that the fields are harmonic and are in phase. Students of the introductory course, who normally are not familiar with Fourier theory, often find it unconvincing to base an important general physical result on the mathematical properties of sinusoidal waves, in addition to having to memorize yet another factoid, namely that the fields are in phase....
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Lec11 - is a B field is increasing so that there is a...

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