Electromagnetic Waves

Chapter 32 Electromagnetic Waves

PowerPoint® Lectures for University Physics, Twelfth Edition – Hugh D. Young and Roger A. Freedman Lectures by James Pazun Modified P. Lam 8_11_2008 Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Topics for Chapter 32 • Maxwell’s equations and wave equation • Sinusoidal electromagnetic waves • Passage of electromagnetic waves through matter • Energy and momentum of electromagnetic waves • Formation of standing electromagnetic wave inside a conducting cavity.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Maxwell’s equations • James Clark Maxwell penned a set of four equations that draw Gauss, Ampere, and Faraday’s laws together in a comprehensive description of the behavior of electromagnetic waves. • The four elegant equations are found at the bottom of page 1093. r Q (E • nˆ )dA = enclosed closed o surface r (B • nˆ )dA = 0 closed surface r r r B E • dl = ( • nˆ )dA Closed Open t loop surface r r r E B • dl = μoIenclosed μoo ( • nˆ )dA Closed Open t loop surface

• Classical Theory: An accelerating charge (eq. a charge moving in a circular motion, a charge oscillates back and forth in an alternating current circuit) creates electromagnetic wave. r r E r B r Concept : B (t) E (t) t t

Quantum Theory: When an excited atom and molecule returns back to the ground state, they generate electromagnetic waves.

1 m (1) Wave speed = 3x108 c oμo s (2) Does not require a medium to carry the wave. r r (3) Transverse wave - E and B are to direction of propagation. Eˆ Bˆ = vˆ r r r r (4) Definite ratio between the magnitudes of E and B : E = c B

Sinusoidal plane wave : r 2 E = ˆj E cos( x 2ft) max r 2 B = kˆ B cos( x 2ft) max c = = f T Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Electromagnetic waves occur over a wide range

• Where wavelength is large, frequency is small. f = c • The range extends from zero to infinite frequency. Common low frequency waves are radio and television waves generated by Ac currents; high frequency waves are X-ray and gamma rays generated by de-excitation of electrons inside an atom and de- excitation of the nucleus.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley The visible spectrum • The visible spectrum is a very small range compared to the entire electromagnetic spectrum. • Visible light extends from red light at 700 nm to violet light at 400 nm.

• Follow Example 32.1. An electromagnetic wave propagates in the negative x-direction, its wavelength is 10.6x10-6 m, the electric field is along the z-direction with maximum E-field=1.5x106 V/m. • Write the equation for E and B-fields.

In a medium such as water or glass, m the electromagnetic wave speed is not c (3x108 ). s

= Ko μ = Kmμo 1 1 c v = = = < c μ KKmoμo KKm

KKm n = index of refraction of the medium. For example : When an electromagnetic wave enters from vacuum into glass, the frequency is unchanged but the new wavelength is different from the orignal wavelength. c v c = , '= = , f f KKm f

Energy is stored in E and B - fields :

Energy 1 2 1 2 u = o E + B volume 2 2μo 2 1 2 1 E 1 2 1 2 Use E = cB u = o E + 2 = o E + o E 2 2μo c 2 2 energy stored in E - field = energy stored in B - field. energy energy Energy intensity = = * wave speed = uc area * time volume

2 2 EB = o E c = o EBc = μo r r This energy flows in the direction given by E B, hence define a energy flow vector (called Poynting vector) r 1 r r S E B μ o

• An electromagnetic wave propagates in the negative x-direction, its wavelength is 10.6x10-6 m, the electric field is along the z-direction with maximum E-field=1.5x106 V/m. • Find the instantaneous energy density, the time average energy density. • Find the instantaneous Poynting vector, the time average intensity.

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley Standing EM waves inside a conducting cavity Similar to standing waves of a vibrating string. The "allowed"wavelengths are fixed by the dimension of the cavity. For example : Two parallel conducting plates are separated by a distance L apart (in the x - direction.). The allowed wavelengths are : 2L 2L 2L = 2L, = , = , ..., = 1 2 2 3 3 n n a set of allowed frequencies: c c fn = = n (n =1,2,3,...) n 2L