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Plane Wave propogation dependent on space and timez

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Hi,

I've been looking at some animations of plane waves, and I really cannot see why a plane wave's electric field is dependent on both t and z. Isn't z a function of t? I would've thought that z could be written in terms of t. Can it? Is there no link between z and t?

$$
\mathbf{E}(x,y,z;t) = \mathbf{E}_o e^{\jmath(\omega t - kz)}
$$

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