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**Statement:**

Consider two dipole antennas, oriented 90degrees apart [imagine the x-y plane, let "a" be the dipole oriented along the x-axis, and the "b" be the dipole oriented along the y-axis]. If "a" dipole radiates [tex]cos(\omega t)[/tex] and "b" dipole radiates [tex]sin(\omega t)[/tex], the field radiated by the two antennas will be circularly polarized:

[tex]\vec{E}(z, t) = E_{0}[cos(\omega t - \beta z)\hat{x} + sin(\omega t - \beta z)\hat{y}][/tex] (#1)

**Relevant Question:**

Ok I almost get it now. Now in terms of a specific distance, say in the [tex]\hat{x}[/tex] direction, the cosine function has traveled a distance [tex]\omega t[/tex] (as did the sine function in it's respective axis). But I don't understand why To find electric field at a given location in the [tex]\hat{z}[/tex] direction, we subtract the distance traveled [tex]\omega t[/tex] by the wave number times distance in z, or [tex]\beta z[/tex] - for each component [tex]\hat{x}, \hat{y}[/tex]. The wave number is the wavelength of the sinusoid per unit distance. What happens when we take this wave number [tex]\beta[/tex] and multiply it by [tex]z[/tex]? What does that represent, I cannot see the relation between the two ([tex]\omega t[/tex] and [tex]\beta z[/tex])?

Does one unit length of [tex]z = 1[/tex] for [tex]\beta z \hat{x}[/tex] and [tex]\beta z \hat{y}[/tex] correspond to a length of [tex]\frac{2\pi}{\lambda}[/tex] in the [tex]\hat{z}[/tex] direction?

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