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Lecture 32 - Energy and momentum. Standing waves

# Lecture 32 - Energy and momentum. Standing waves - Energy...

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1 Lecture 32 Energy and momentum Energy and momentum. Standing waves. Energy in a EM wave Energy density due to an electric field: 2 0 1 2 u E Energy density due to a magnetic field: 2 0 1 2 u B Energy density for an EM wave: 2 2 0 0 1 1 2 2 u E B but 0 0 B E cB   2 2 0 0 0 0 1 1 2 2 u E E   2 0 u E Energy density equally split between E, B fields Energy transport How much energy goes through a surface of area A in time dt ? Energy in this “box”: y x propagation cdt 2 dU udV E Acdt z 0 Energy flow per unit time and per unit area: 2 0 1 dU S cE A dt 0 EB Definition: Poynting vector 0 1 S E B Energy flow per unit time and per unit area I S Intensity: ACT: Plane harmonic wave P At the time shown, the magnetic field at point P (on the y axis) is: 1. B max i 2. B max j 3. 0 0% 0% 0% 60

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2 x y Propagation P At the time shown, the magnetic field at point P (on the y axis) is: A. B max i B. B max j C. 0 z x z y E/B are the same at all points in each yz plane! Propagation direction is , so is in the direction and is in the direction E B E x B y Energy in the harmonic wave 2 max max 1 1 ˆ ˆ cos S E B E B kx t j k max ˆ cos E E kx t j max ˆ cos
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Lecture 32 - Energy and momentum. Standing waves - Energy...

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