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## 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]?