(a) Assume E = (E, E, E) and B = (B, B2, B3) solves Maxwell's equations...

 

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(a) Assume E = (E¹, E², E³) and B = (B¹, B2, B3) solves Maxwell's equations Et = curl B B₁ = -curl E div B = 0 div E = 0 Ett - AE = 0, Btt - AB=0 Show that (b) Assume that u = (u²,u², u³) solves the evolution equations of the linear elasticity U-μAu-(λ +μ)D(divu) = 0 in R³ x (0,00) Show w:= div u and w curl u each solves wave equations, but with different propagation speed. (a) Assume E = (E¹, E², E³) and B = (B¹, B2, B3) solves Maxwell's equations Et = curl B B₁ = -curl E div B = 0 div E = 0 Ett - AE = 0, Btt - AB=0 Show that (b) Assume that u = (u²,u², u³) solves the evolution equations of the linear elasticity U-μAu-(λ +μ)D(divu) = 0 in R³ x (0,00) Show w:= div u and w curl u each solves wave equations, but with different propagation speed.

Answer rating: 100% (QA)

solution a To show that Ett E 0 and Btt B 0 we need to differentiate the given equations and apply appropriate vector calculus identities Starting with the first equation E curl B we can take the curl ... View the full answer