# Velocity of propagation of an EM field in vacuum

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1. Feb 20, 2016

### It's me

1. The problem statement, all variables and given/known data

In a region of empty space, the magnetic field is described by $\vec{B} = B_0e^{ax}\sin{(ky-\omega t)} \hat{z}$. Find the speed of propagation $\vec{v}$ of this field.

2. Relevant equations

$\Delta \vec{B} = \frac{1}{v^2}\frac{d^2\vec{B}}{dt^2}$ , $k=\frac{\omega }{ v}$

3. The attempt at a solution

I'm not sure of a way to calculate the velocity. Do I have to take into account the equation, or because the wave is propagating in empty space can I simply say $v=c$? And I know the direction of propagation would be $\hat{y}$ if the term $e^{ax}$ didn't exist, but is it still $\hat{y}$ with it? I really don't understand how that term affects the velocity of propagation.

2. Feb 20, 2016

### phyzguy

Try plugging your expression for B into Maxwell's equations.

3. Feb 21, 2016

### It's me

I did that and got #\vec{E}#, but I still don't understand what equation to use to get the velocity.