Lect26_[Compatibility_Mode]

Lect26_[Compatibility_Mode] - Physics 344 Foundations of...

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Physics 344 Foundations of 21 st Century Physics: Relativity, Quantum Mechanics and heir Applications Their Applications Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Shuo Liu Office: PHYS 283 [email protected] Office Hours: If you have questions, just email us to make an ppointment. e enjoy talking about physics! appointment. We enjoy talking about physics! Reading: Sections 24.1 and 24.2 in Matter & Interactions, Vol. II, 2 nd Edition
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Recitation Recap The second and third quickly established the scales of frequency and wavelength or wavenumber of the light and higher frequency (energy) electromagnetic radiation that will concern us. The intent of the first problem was to connect the physical structure and the mathematical representation we developed of linearly polarized plane waves. asked you to plot values of at points r G G 2,, 0 k ππ = G It asked you to plot values of at points in the xy plane with integer coordinates. kr For we find these values. 0 2 π 4 π - π 3 π π It then asked you to connect points with the same values. hese correspond to locations where the 0 2 π 4 π -2 π These correspond to locations where the y component of the electric field of a wave like the one we showed satisfies Maxwell’s equations has its maximum positive values - 3 π at time t = 0 ˆ (, ,,) c o s ( ) Exyzt E k r t j ω =⋅ G G G ˆ c o s ( ) B xyzt B tk G G G
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We noted that these lines are perpendicular to because the position vectors r G k G of the points along them all have the same projection onto . k G Adding lines to the figure where the y component of the electric field of the wave ˆ ) ( ) t E k t j G G G ˆ G G G has its maximum negative values at time t = 0 brings out the overall structure of the plane wave field more clearly. ( ,,, cos () E x y z tE r tj ω = ⋅− ( ) cos B xyz tB k r tk = 0 2 π 4 π Notice that the distance between lines with phases that differ by 2 π is the wavelength λ . - π 3 π π k G λ Notice, too, that if we increased the magnitude of by a factor of 2, the values of that we’ve plotted would all double, k G kr G G 0 2 π 4 π -2 π so, the spacing between lines with phases that differ by 2 π , i.e., the wavelength λ , would be cut in half. Indeed, - ππ 3 π 2 || k π = G
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Finally, we can use our figure to understand how the wave’s field pattern moves as time advances. The original figure showed the locations of the maximum and minimum E y values for the field at time zero. Half a wave period later at t = T /2 we have cos( /2) cos () E E kr T E ω π = ⋅− = G G G G 0 2 π 4 π y which means that at the origin, for example, the phase is – π instead of 0 as before. his is true for all of the points along the - π 3 π π This is true for all of the points along the wavefront where the phase was initially zero.
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This note was uploaded on 11/26/2010 for the course PHYS 344 taught by Professor Garfinkel during the Spring '08 term at Purdue.

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Lect26_[Compatibility_Mode] - Physics 344 Foundations of...

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