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 uE Energy density due to a magnetic field: 2 0 1 2 uB Energy density for an EM wave: 22 0 0 11 B  but 00 EcB   0 0 E  2 0 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 Sc Adt 0 EB Definition: Poynting vector 0 1 SE  Energy flow per unit time and per unit area IS Intensity: ACT: Plane harmonic wave P At the time shown, the magnetic field at point P (on the axis) is: 1. max i 2. 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 axis) is: A. B max i 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 EB Ex By Energy in the harmonic wave  2 max max 11 ˆ ˆ cos SE BE k t j   max ˆ cos EE kx tj  max ˆ cos BB kx tk 00 2 max max 0 1 ˆ cos kx ti 2 max max max max cos 2 IS kxt    Direction +
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## This note was uploaded on 09/21/2011 for the course PHYS 222 taught by Professor Johnson during the Spring '07 term at Iowa State.

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

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