Prozorov_24-25

Prozorov_24-25 - PHYSICS 222 Introduction to Classical...

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Unformatted text preview: PHYSICS 222 Introduction to Classical Physics II Prof. Ruslan Prozorov Iowa State University Fall 2011 LECTURES 24 and 25 Electromagnetic waves. y Faraday’s law: Line integral over a rectangular circuit (sides Δx, a) in the xy plane.: Ey x x ,t a E y x ,t a E dl Ey x,t a Bz x,t Ey x x,t x Bz x x,t z x If Δx is small B a x x x d B E dl dt Bz x ,t t Bz x ,t d B a x dt t Bz x ,t dx ~ aBz x ,t x E y x x ,t E y x ,t a a x E y x x ,t E y x ,t x x 0 PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University Bz x ,t Bz x ,t t t E y x ,t x 19 and 21 October 2011 2 y Ampere’s law: Line integral over a rectangular circuit (sides Δx, a) in the xz plane: Ey x,t Bz x x ,t Bz x ,t a 0 0a x 0 0 E y x ,t t a Bz x,t z d E B dl 0 0 dt Ey x x,t x Bz x x,t x E y x ,t t Bz x x ,t Bz x ,t x 0 0 x 0 E y x ,t t PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University Bz x ,t x 19 and 21 October 2011 3 0 0 E y t Bz 0 0 x t Bz t 2Bz 2Bz t x x t x Bz t 2E y t 2 2Bz t x E y x x 0 0 E y x 0 0 2y 1 2y v 2 t 2 x 2 x 2 2Bz t 2 2Bz x 2 This is a wave with speed This value is essentially identical to the speed of light measured by Foucault in 1860! (3108 m/s) Maxwell identified light as an electromagnetic wave. PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University t 2 2E y Similarly, we can obtain Remember the wave equation from 221? 2E y v 1 0 0 19 and 21 October 2011 4 using Maxwell Equations PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 19 and 21 October 2011 5 in vacuum A A 2 A B E E , E 0, B 0 0 t t 2 E 2 E E E B 0 0 2 t t 2E 2E 2 2 0 0 2 2 E 0 2 c E 0, t t 1 1 8 m c 2.9979×10 0 0 s 4 ×107 ×8.85×1012 PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 19 and 21 October 2011 6 plane electromagnetic wave Let us assume that we have: • E-field in the y direction, uniform along yz plane • B-field in the z direction, uniform along yz plane • propagation in the x direction 2 Ey d 2 Ey 2E 2 2 c E 0 c2 0 2 2 2 t dx t 2 B 2 2 2 Bz d 2 Bz 2 c B 0 c 0 2 2 2 t t dx PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 19 and 21 October 2011 7 harmonic solution Let’s try a wave-like solution: E y Emax cos kx t 2 Ey c2 d 2 Ey 0 t dx 2 Emax cos kx t c 2 k 2 Emax cos kx t 0 2 2 2 c 2 k 2 0 with Maxwell equation: k 2 c 2 f f c c dE y B E , E kEmax sin kx t z t dx dE y dBz E kEmax sin kx t z dt dx k Bz Emax cos kx t Bz Emax E cos kx t , Bmax max c c PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 19 and 21 October 2011 8 alternatively with another Maxwell equation: y dB 1 E , B z y c 2 t dx dBz 1 E y 2 2 Emax sin kx t dx c t c B Bz Emax cos kx t z kc 2 E Bz max cos kx t c PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University x 19 and 21 October 2011 9 how is the EM wave moving? Let’s focus on one point (e.g. when E=Emax) and see how it behaves in time it is moving with velocity c in a positive x direction! E y Emax cos kx t 1 kx t 0 x t k x ct PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 19 and 21 October 2011 10 harmonic EM waves summary for harmonic EM wave propagating in the x direction: E Emax cos kx t B Bmax cos kx t with 2 k 2f c f 1 k 0 0 E is perpendicular to B propagation direction is E B wave speed is c 1 0 0 E and B are always in phase E cB (magnitudes) PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 19 and 21 October 2011 11 In-class example: radio stations Radio stations broadcast at frequencies that range from 540 kHz (low end of AM band) up to 108 MHz (high end of FM band). What is the range of wavelengths associated with these frequencies? c f max min 3 108 m/s 540 10 Hz 3 3 108 m/s 108 10 Hz 6 555 m 2.78 m significant range! Very different physics (we’ll come back to this: diffraction and reflection) PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 19 and 21 October 2011 12 EM waves not in vacuum E field inside a material is characterized by dielectric constant or the dielectric permittivity 0 Similarly: B field inside a material is characterized by relative permeability m or the permeability 0 EM wave speed in general: v 1 c m c n n m PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 1 always Refraction index 19 and 21 October 2011 13 electromagnetic waves spectrum o Where wavelength is large, frequency is small. o The range extends from low energy and frequency (radio and television) to high energy and small wavelength (gamma rays). PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 19 and 21 October 2011 14 nomenclature γ = Gamma rays HX = Hard X-rays SX = Soft X-Rays EUV = Extreme ultraviolet NUV = Near ultraviolet Visible light NIR = Near infrared MIR = Moderate infrared FIR = Far infrared Radio waves: EHF = Extremely high frequency (Microwaves) SHF = Super high frequency (Microwaves) UHF = Ultrahigh frequency VHF = Very high frequency HF = High frequency MF = Medium frequency LF = Low frequency VLF = Very low frequency VF = Voice frequency ULF = Ultra low frequency SLF = Super low frequency ELF = Extremely low frequency PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 19 and 21 October 2011 15 The visible spectrum o The visible spectrum is a very small range compared to the entire electromagnetic spectrum. PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 19 and 21 October 2011 16 energy of an EM wave, the Poynting vector S PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 1 E B 0 19 and 21 October 2011 17 Poynting vector for planar EM wave S 1 1 ˆ ˆ x y E B 0 0 0 0 ˆ z Ey 0 0 E y Bz Bz 0 ˆ x Maxwell eqns. conservation of EM energy – Poyinting theorem u 1 B2 divS 0, u 0 E 2 t 2 0 E y Bz 0 0 t x E y Bz t x E B B d E y Bz d Bz Bz d E y 0 E y ty z tz Ey dx 0 dx 0 0 dx 0 E y Bz Bz u 0 Ey t t 0 t divS PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 19 and 21 October 2011 18 E y Bz E B ˆ S x 0 0 E y Emax cos kx t Bz Bmax cos kx t Emax Bmax S x x, t cos 2 kx t 1 Bmax Emax c 0 Emax Bmax 1 0c 2 1 c 2 2 S t dt cos kx t dt 20 B max 2 E max T 0 0 T 0 T S ave T PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 19 and 21 October 2011 19 “Solar wind” – EM pressure electromagnetic pressure S ave P c PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 19 and 21 October 2011 20 standing EM waves PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 19 and 21 October 2011 21 EM waves interact with matter in bundles It turns our EM waves can interact with matter in portions called PHOTONS. for every wavelength, there are photons with energy U and momentum p U pc hf hc hf h p k c 34 h 6.63... 10 J s = h 2 PHYS222 - Lecture 24 & 25 - Prof. Ruslan Prozorov - Iowa State University 19 and 21 October 2011 22 ...
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This note was uploaded on 11/14/2011 for the course PHYS 5863005 taught by Professor Meyer during the Fall '09 term at Iowa State.

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