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Introductory Physics Homework Help
Consistency of Faraday's Law and Electric Field Equation in Optics
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[QUOTE="Blue Kangaroo, post: 6058179, member: 617182"] [h2]Homework Statement [/h2] Suppose that an electric field is given by E(r,t)=E[SUB]0[/SUB]cos(k·r−ωt+φ), where k⊥E[SUB]0[/SUB] and φ is a constant phase. Show that B(r,t)=((k×E)/ω)B(k⋅r-ωt+φ) is consistent with ∇×E=-∂B/∂t [h2]Homework Equations[/h2] ∇×E=-∂B/∂t [h2]The Attempt at a Solution[/h2] I know I have to take the curl of E, but I'm not sure how to go about doing it. ∂E/∂t would be ωE[SUB]0[/SUB]sin(k⋅r-ωt+φ) and ∂E/∂r would be -kE[SUB]0[/SUB]sin(k⋅r-ωt+φ), but I'm not sure if that helps. Also, by my calculation, -∂B/∂t= (k×E)cos(k⋅r-ωt+φ). Any help would be greatly appreciated. [/QUOTE]
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Introductory Physics Homework Help
Consistency of Faraday's Law and Electric Field Equation in Optics
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