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An oscillating current is producing an electromagnetic wave. The region shown enclosed by a dotted box (not to scale) is far from the current. In it, the field produced is well approximated by a plane wave traveling in the z direction and having its E-field pointed along the x-direction (using the coordinate system shown).

1. I perform a series of measurements of the electric field at the origin and obtain a result which points in the x-direction and is well represented by the function
   E(t) = E₀ cos(wt).

   What result would I find if instead of at the origin, I repeated my experiment at the point with coordinates {0,0,z}? Explain how you know.

2. What result would I get if I made my measurements at the point in the box with coordinates {2, 3, z}cm. (The point is still well within the dotted box.)

3. For what values of z would I find exactly the same result as I found at the origin?

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