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(a) (3 marks) What are the three vectors in an EM wave?

(a) (3 marks) What are the three vectors in an EM wave?

(b) (5 marks) In the lectures it was shown that the electric field can be written as E = ˆeE0ei(k·r−ωt)

Use a similar method to show that the magnetic field can be written as B = ˆ bB0ei(k·r−ωt) CLARIFICATION: You don’t need to derive B here, just write it out (expand it) and explain what each term is, like we did for E in the lecture.

(c) (4 marks) We then used some of Maxwell’s equations in a vacuum, ∇· E = 0 and ∇· B = 0 to show that ˆe ⊥ k and ˆ b ⊥ k.

What does this say about how the direction of the three vectors in an EM wave are linked?

(d) (3 marks) If you have the direction of two of these vectors, how would you find the direction of the third?

(e) (10 marks) Show that ∇×E = ± iE0ei(k·r−ωt)(ˆe×k) (f) (5 marks) Find the equivalent equation for ∇×B


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