Problem 1 In class we considered a plane parallel sinusoidal wave of the form E Eo cos kz wt B Boy cos kz wt where Eo and Bo are

Question

Problem 1 In class we considered a plane parallel sinusoidal wave of the form E Eo cos kz wt B Boy cos kz wt where Eo and Bo are amplitudes k is the magnitude of a wave number and w is an angular frequency The y component of the Maxwell s equation involving VX E in vacuum is d dz and the component of the equation involving V x B is d d dy dz d B B Hofo Ez dt Ex d Ez dx d dt 1 2 By 3 4 Show by taking the derivatives and plugging in that the given forms for the electric and magnetic fields can satisfy these equations provided that there is some particular relationship between Eo and Bo and some particular relationship between k and w What are those relationships You should be able to write an expression for the ratio Eo Bo and an expression for the ratio w k Both of these expressions should depend only on fundamental constants w Fo and C

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