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adichy
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Homework Statement
The electric and magnetic fields in a plane wave propagating in free-space in the z-direction can we represented by (in complex-exponential notation)
E(x, y, z, t) = E_0 e^i(kz−wt+d ) and B(x, y, z, t) = B_0e^i(kz−wt+d )
Starting with the Ampère-Maxwell law, ∇ x B =μ_0 ε_0 dE/dt , show that E_0 = −c(z×B0).
Homework Equations
The Attempt at a Solution
I'm only having problems when I do curl B (differentiating E is no problem). I'm using the matrix method, but by just looking, it seems like it should be zero since B is in the z direction and there's no field in the x or y direction i.e
x_______y________z
d/dx___d/dy_____d/dz
0_______0____B_0e^i(kz−wt+d )
I should be getting something like ike^(...), but I'm not. Any insight would be helpful
Thanks
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