[tex]\vec E\;=\; \hat x E_{x0}\cos(\omega {t} -kz)\;+\;\hat y E_{y0}\cos(\omega{t}-kz+\delta)[/tex](adsbygoogle = window.adsbygoogle || []).push({});

For z=0, this is a vector that trace out an ellipse with time t.

I want to

1) to verify that using the definition of differential calculus, we can find the length of the major and minor axis by finding the maximum and minimum of the the derivative of the [itex]\vec E[/itex]. This is by taking the derivative of [itex]\vec E[/itex] and let the derivative equal to zero to get the minimum and maximum value.

2) Find a way to get the maximum and minimum. I don't know how to do this. This is my work:

[tex]\frac {\partial \vec E}{\partial t}\;=\; -\hat x \omega E_{x0}\sin(\omega {t} -kz)\;-\;\hat y E_{y0}\sin(\omega{t}-kz+\delta)[/tex]

For [itex]\frac {\partial \vec E}{\partial t}\;=\;0[/itex], both components of x and y has to be zero. I don't know how to do this. Please help.

thanks

Alan

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# Finding the length of the major and minor axis of ellipse.

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