Maxwell's Equations and Electromagnetic Waves, Slides of Physics

Download Maxwell's Equations and Electromagnetic Waves and more Slides Physics in PDF only on Docsity! Electromagnetic Waves 1. Maxwell’s equations & their solutions 2. Electromagnetic energy and their spectral distribution 3. Review of Chapters 29-34 Docsity.com                  AEsB ABsrE ArB ArE dr dt dId dr dt dd d Qd in in 000 0 0   t t         EJB BE B E 000 0 0    Full Maxwell’s equations  Docsity.com      ctxk c EtxBB ctxkEtxEE zz yy   cos),( cos),( max max Plane wave solution to Maxwell’s  equations, far from sources:  Additional comments:  For this solution, the y direction is called the  polarization  direction (the E field  orientation)    This is a periodic wave, where k=2/and    represents the wavelength and the frequency of the  wave is kc==2f. Docsity.com Homework hint: The figure below shows a plane electromagnetic sinusoidal wave propagating in the x direction. Suppose the wavelength is 58.0 m and the electric field vibrates in the xy plane with an amplitude of 18.0 V/m. y (a) Calculate the frequency of the wave. MHz = (b) Calculate the magnetic field B when the electric field has its maximum value in the negative y direction. magnitude nT direction ---Select— v = (c) Write an expression for B with the correct unit vector, with numerical values for Biyaxt Kr and @, and with its magnitude in the form B=B _ cos (kx — of). max (Assume B is measured in nT, x is measured in m and ¢ in s.) magnitude cos ( a t) nT direction -—-Select— v Docsity.com Energy carried by electromagnetic waves:  222 0 m W sm J sm mN sm NT C N m/AmpT 1 :units 1 : vectorPoynting           BES          iS ˆcos cos),( cos),( 2 0 2 max max max ctxk c E ctxk c EtxBB ctxkEtxEE zz yy     Docsity.com c S BEu BEu u avg avg avg    2 1 2 1 4 1 4 1 2 1 2 1 energy Magnetic energy Electrical :densityenergy neticElectromag 2 max 0 2 max0 2 max 0 2 max0 2 0 2 0       BE Energy density within electromagnetic wave:  Docsity.com Sources of electromagnetic radiation                   AEsB ABsrE ArB ArE dr dt dId dr dt dd d Qd in in 000 0 0   t t         EJB BE B E 000 0 0    Need accelerating charges to produce E‐M radiation  Docsity.com Radiation from antenna’s The electric field lines resemble those of an electric dipole (shown in Fig. 23.20). Docsity.com Electromagnetic spectrum Frequency, Hz 1022 102! 1 1020 1019 1018 1017 1016 1015 1014 1018 101? 10! 1019 10° 10° 107 10° 10° 104 10° A | I Gamma rays Wavelength Microwaves Long wave Radio waves \ \ \ Y lpm Imm lem lkm The visible light spectrum is expanded to show details of the colors. ~700 nm Adjacent wave types exhibit some overlap of frequencies. Docsity.com Comment about solar energy Technology to capture and use electromagnetic radiation from the sun and use it as a heat source or as a generator of voltage in special semiconductor devices (see web page from Prof. Wesley Henderson from NCSU: http://www.che.ncsu.edu/ILEET/CHE596web _ Fall2011/ 21_CHE596-015 2011-11-15 Renewables. pdf Docsity.com  ‘Aatry Rabers Octet 20.2008 ‘Tis map wa proceed by the National Renewable Crengy Laboratory forthe US. Cepartmeet of Cay B) } SVs U N | i] is RS | TY Source: Frontiers of Research in Renewable Energy - Dan Arvizu (Oct 8, 2009) 3 Docsity.com  Problem solving steps 1. Visualize problem – labeling variables 2. Determine which basic physical principle(s) apply 3. Write down the appropriate equations using the variables defined in step 1. 4. Check whether you have the correct amount of information to solve the problem (same number of knowns and unknowns). 5. Solve the equations. 6. Check whether your answer makes sense (units, order of magnitude, etc.). Docsity.com Comment on AC circuits:  I1  I2  I3  321 32 2 1 0 0 III C Q dt dIL dt dILRI   E Solution method:  1. Transform differential  equation in to algebraic  equation using trig or  complex functions  2. “Solve” algebra problem  3. Analyze for physical  solution    Docsity.com Example using Ampere’s law and Ampere‐Maxwell law:          First consider Ampere’s law and a wire with uniform current I  inId 0 sB 2 20 2 2 2 02 2 1 0 2 2 01 1 2 2 :at 2 2 :at R IrB πR πrIrB RrB r IB πR πRIrB RrB         Docsity.com Homework hint: Consider the situation shown in the figure below. An electric field of 300 V/m is confined to a circular area d = 10.5 cm in diameter and directed outward perpendicular to the plane of the figure. Consider that the field is increasing at a rate of 18.8 V/m-<s. (a) What is the direction of the magnetic field at the point P, r = 13.6 cm from the center of the circle? © upwards © downwards (b) What is the magnitude of the magnetic field at the point P, r = 13.6 cm from the center of the circle? T Docsity.com                  AEsB ABsrE ArB ArE dr dt dId dr dt dd d Qd in in 000 0 0   t t         EJB BE B E 000 0 0    Full Maxwell’s equations  Lorentz force law:   BvEF  q Docsity.com