HW-12 - HW-12 1. In the complex notation there is a clever...

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Unformatted text preview: HW-12 1. In the complex notation there is a clever device for finding the time average of a product. f (r , t ) A cos(k r t a ) and g (r , t ) B cos(k r t b ) . Suppose Show that ~~ ~ ~ fg (1/ 2) Re( fg *) , where f and g are the complex of f and g and the star denotes complex conjugation. 2. We know that free charges inside a conductor will eventually move to the conductor surface. Consider a free charge initially placed inside a conductor at t=0. Show that the free charge density f will dissolve exponatially with time. Express the characteristic time needed to dissolve the charge in terms of the conductor’s dielectric constant and the conductivity . 3. In the lecture, I discussed the reflection and transmission of p wave. Using the coordinate setup in the following figure (s//y), derive the reflection and transmission coefficients for the s wave, and verify that R+T=1. Taking 1 2 0 . ...
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