Electromagnetic Wavs - General Physics - Lecture Slides, Slides of Physics

Download Electromagnetic Wavs - General Physics - Lecture Slides and more Slides Physics in PDF only on Docsity! Chapter 29: Electromagnetic Waves • Transformers - demo • Maxwell’s equations • Electromagnetic waves • Wave equations • Speed of light • Relations between quantities • Energy flux and intensity Reading: up to page 515 in the text book (Ch. 28/29) Docsity.com Transformers Soft iron • Flux the same on both sides, but number of turns, N, is different • Total flux through primary and secondary coils depends on N1 and N2 V 1 = N 1 !; V 2 = N 2 !; " V 2 V 1 = N 2 N 1 Docsity.com I I I I Maxwell’s displacement current ! B !d ! l = µ o I enc" = µo#J = µ o ! J !d ! A" Stokes’ theorem: The choice of surface should not matter Docsity.com I I I I Maxwell’s displacement current ! B !d ! s = µ o I + I d( )" I d = ! o d! E dt ! B !d ! l = µ o I + µ o" !o d# E dt Stokes’ theorem: The choice of surface should not matter Docsity.com Maxwell’s equations The main thing to note here is the symmetry in the last two equations: a time varying magnetic field produces an electric field; similarly, a time varying electric field produces a magnetic field. Docsity.com Maxwell’s equations guarantee that electric and magnetic fields are perpendicular to each other and perpendicular to the direction of propagation; they are polarized. Spherical waves Plane waves ! E! ! B Electromagnetic waves Docsity.com Maxwell’s equations in vacuum !E = ! E !d ! A! = 0 !B = ! B "d ! A"# = 0 ! B !d ! l = µ o ! o d" E dt"# ! E !d ! l =" # d$ B dt !" ! B = µ o ! o d ! E dt # $ % %% & ' ( (( !" ! E =#d ! B dt $ % & & & ' ( ) ) ) Stokes’ Theorem: Gives differential form of Maxwell’s equ’ns Docsity.com Let there be light!! !" ! B = µ o ! o d ! E dt !" ! E =#d ! B dt Stokes’ Theorem: Gives differential form of Maxwell’s equ’ns Maxwell’s equations in vacuum can be solved simultaneously to give identical differential equations for E and B: !2 ! E = µ o ! o "2 ! E "t 2 and !2 ! B = µ o ! o "2 ! B "t 2 !2 = "2 "x 2 + !2 !y2 + !2 !z 2 The Laplacian differential operator The Electromagnetic Wave Equations Docsity.com Review of waves (PHY2048) 2k π λ = k is the angular wavenumber. Tr an sv er se w av e 2 T πω = w is the angular frequency. 1 2 f T ω π = = v = !! k = ! " T = ! f " frequency velocity my(x,t) = Asin(kx ±! t +") Amplitude Displacement Phase } Phase shift angular wavenumber angular frequency Docsity.com Electromagnetic waves x Direction of motion ! E x,t( )= Ep sin kx !!t( ) ĵ ! B x,t( )= Bp sin kx !!t( )k̂ • The E and B fields are still related via Ampère’s and Faraday’s laws. • For a plane wave traveling in the x direction (see text): Docsity.com Electromagnetic waves • The E and B fields are still related via Ampère’s and Faraday’s laws. • For a plane wave traveling in the x direction (see text): !E z !x = !B y !t , !E y !x =! "B z !t , E x = B x = 0 x Direction of motion Docsity.com