Humor in the Workplace: Benefits and Challenges

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Homework Statement

Part a is not an issue, I have that solved. I'm confused with part b (and c since i cant get b), and need someone to explain this to me... I do not even know where to start. Although, I do know that k E and B are orthogonal to one another. Evidently, this means that the dot product between k and E will be 0, as they are perpendicular. I just don't know how to use Maxwells Equations to prove this.
Thanks!

Relevant Equations

Maxwells Equation

 

[Delta2]

The two Maxwell's equations you going to use for this are
1) Gauss's law in differential form $$\nabla\cdot E=0$$ (with no sources)

2)Maxwell-Faraday's law in differential form $$\nabla\times E=-\frac{\partial B}{\partial t}$$

Start by pluging in 1) the expression for electric field you got from doing part a) and try to calculate $\nabla\cdot E$. You might find the following identity useful $\nabla\cdot( \phi E_0)=E_0\cdot\nabla\phi$ where $\phi(x,y,z,t)$ is a scalar function and $E_0$ is a constant vector independent of x,y,z,t.

When plugging the expression you got from a) for E in 2) you might find useful the following identity
$\nabla\times (\phi E_0)=\nabla\phi\times E_0$