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ParoxysmX
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Homework Statement
Consider the electric field E(t,x,y,z) = Acos(ky-wt)k
1. Find a magnetic field such that [itex]\partial_t[/itex]B + [itex]\nabla[/itex] X E = 0
2. Show that [itex]\nabla[/itex] . E = 0 and [itex]\nabla[/itex]. B = 0
3. Find a relationship between k and w that enables these fields to satisfy
[itex]\nabla[/itex] X B = [itex]\mu_{0}[/itex][itex]\epsilon_{0}[/itex][itex]\frac{\partial E}{\partial t}[/itex]
The Attempt at a Solution
Really the problem here is the first one. I understand (sort of) the curl operator, but how do you find [itex]\nabla[/itex] X E? Would you start with a matrix of
[i j k
0 kAcos(ky-wt) 0
0 0 Acos(ky-wt)]
Then find the determinant, which is Acos(ky-wt)(1+k)i - 0j + 0k?
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