- #1
raggle
- 8
- 0
Homework Statement
Given [itex]\textbf{E}(z,t) = E_{0}cos(kz+ωt)\textbf{i}[/itex]
Find B
Homework Equations
∇ x E = -[itex]\frac{\partial\textbf{B}}{\partial t}[/itex]
The Attempt at a Solution
Taking the curl of [itex]\textbf{E}[/itex] gives [itex](0, -ksin(kz+\omega t), 0)[/itex]
so
[itex]\frac{\partial\textbf{B}}{\partial t} = (0,ksin(kz+\omega t),0)[/itex]
I'm not too confident integrating this, I got
[itex]\textbf{B} = (f(z),-\frac{k}{\omega}cos(kz+\omega t), g(z)) + \textbf{c}[/itex]
where c is a constant of integration.
Is this right? The next part of the question asks for the poynting vector and it seems like a lot of work calculating [itex]\textbf{E} \times \textbf{B}[/itex] , would i be allowed to set [itex]f = g = 0[/itex]?