Lecture25

Lecture25 - Physics 344 Foundations of 21 st Century...

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Unformatted text preview: Physics 344 Foundations of 21 st Century Physics: Relativistic and Quantum Systems Instructor: Dr. Mark Haugan Office: PHYS 282 [email protected] TA: Dan Hartzler Office: PHYS 7 [email protected] Grader: Fan Chen Office: PHYS 222 [email protected] Office Hours: If you have questions, just email us to make an appointment. We enjoy talking about physics! Help Session: Thursdays 2:00 – 4:00 in PHYS 154 Reading: Chapters 2 and 3 in Six Ideas that Shaped Physics, Unit Q for x ≈ r >> y and z Monochromatic Radiation A charge forced to execute a sinusoidal oscillation emits monochromatic radiation. Far from the source at points in the neighborhood of the x axis the radiation field is well approximated by the linearly polarized sinusoidal plane wave that we showed satisfies Maxwell’s equations. 2 1 4 radiation qa E c r π ε ⊥- = a a ˆ ( , , , ) cos( ) B t x y z B kx t z ϖ φ =- + a x y ˆ ( , , , ) cos( ) E t x y z E kx t y ϖ φ =- + a ˆ ( , , , ) cos( ) B t x y z B kx t z ϖ φ =- + a ˆ ( , , , ) cos( ) E t x y z E kx t y ϖ φ =- + a The Phase of a Monochromatic Plane Wave The cosine’s argument in our representation of a linearly polarized sinusoidal plane wave is called its phase, ( , , , ) t x y z kx t φ ϖ φ =- + We’ve added a phase constant Φ that allows us to adjust where the maximum values of the wave’s electric and magnetic field components are located at a specific time and when they occur at a specific location. φ = 2 π φ = For example, these plots of the E y field at x = 0 as a function of time at show the effect of a phase constant Φ = π /2 . ˆ ( , , , ) cos( ( , , , )) B t x y z B t x y z z φ = a ˆ ( , , , ) cos( ( , , , )) E t x y z E t x y z y φ = a ( , , , ) t x y z kx t φ ϖ φ =- + 2 π 4 π-2 π-2 π-2 π 2 π 2 π 4 π 2 π-2 π 4 π y x 4 π-2 π-2 π-2 π-2 π y x 2 π 2 π 2 π 2 π-4 π-4 π-44 π-4 π Field components have the same value on planes with the same phase value. Phase values at t = 0 with Φ = 0 The field pattern “travels” right when k > 0 because as t increases, the location of the plane with a given phase value has a larger x value. Phase values at t = T with Φ = 0 λ ˆ ( , , , ) cos( ( , , , )) B t x y z B t x y z z φ = a ˆ ( , , , ) cos( ( , , , )) E t x y z E t x y z y φ = a The Wave Vector of a Monochromatic Plane Wave Expressing the wave’s phase in terms of a vector pointing in the direction the wave travels makes it easy to represent a generic linearly polarized monochromatic plane wave field....
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This note was uploaded on 12/09/2011 for the course PHYS 344 taught by Professor Garfinkel during the Fall '08 term at Purdue.

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Lecture25 - Physics 344 Foundations of 21 st Century...

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