Electromagnetic Waves

Transcription

1 Chapte 32 Electomagnetic Waves PowePoint Lectues fo Univesity Physics, Twelfth Edition Hugh D. Young and Roge A. Feedman Lectues by James Pazun Modified P. Lam 8_11_2008

2 Topics fo Chapte 32 Maxwell s equations and wave equation Sinusoidal electomagnetic waves Passage of electomagnetic waves though matte Enegy and momentum of electomagnetic waves Fomation of standing electomagnetic wave inside a conducting cavity.

3 Maxwell s equations James Clak Maxwell penned a set of fou equations that daw Gauss, Ampee, and Faaday s laws togethe in a compehensive desciption of the behavio of electomagnetic waves. The fou elegant equations ae found at the bottom of page ( E n ˆ ) da = Q enclosed closed suface ( B n ˆ ) da = 0 closed suface Closed loop o E d l = ( B n ˆ )da Open t suface B d l = μ I μ ( E o enclosed o o t Closed loop Open suface ˆ n )da

4 Ceating electomagnetic waves Classical Theoy: An acceleating chage (eq. a chage moving in a cicula motion, a chage oscillates back and foth in an altenating cuent cicuit) ceates electomagnetic wave. Concept : E t B (t) B t E (t) Quantum Theoy: When an excited atom and molecule etuns back to the gound state, they geneate electomagnetic waves.

5 Popeties of Electomagnetic waves in vacuum 1 m (1) Wave speed = 3x10 8 o μ o s c (2) Does not equie a medium to cay the wave. (3) Tansvese wave - E and B ae to diection of popagation. E ˆ B ˆ = v ˆ (4) Definite atio between the magnitudes of E and B : E = c B

6 Spheical wave and Sinusoidal Plane waves Sinusoidal plane wave : E = ˆ j E max cos( 2 x 2 f t) B = k ˆ B max cos( 2 x 2 f t) c = T = f

7 Electomagnetic waves occu ove a wide ange Whee wavelength is lage, fequency is small. f = c The ange extends fom zeo to infinite fequency. Common low fequency waves ae adio and television waves geneated by Ac cuents; high fequency waves ae X-ay and gamma ays geneated by de-excitation of electons inside an atom and deexcitation of the nucleus.

8 The visible spectum The visible spectum is a vey small ange compaed to the entie electomagnetic spectum. Visible light extends fom ed light at 700 nm to violet light at 400 nm.

9 Numeical example. Follow Example An electomagnetic wave popagates in the negative x-diection, its wavelength is 10.6x10-6 m, the electic field is along the z-diection with maximum E-field=1.5x10 6 V/m. Wite the equation fo E and B-fields.

10 Popagation of electomagnetic wave in a linea medium In a medium such as wate o glass, m the electomagnetic wave speed is not c (3x10 8 s ). = K o μ = K m μ o v = 1 μ = 1 c = < c KK m o μ o KK m KK m n = index of efaction of the medium. Fo example : When an electomagnetic wave entes fom vacuum into glass, the fequency is unchanged but the new wavelength is diffeent fom the oignal wavelength. = c f, '= v f = c KK m f,

11 Enegy in an EM wave, the Poynting vecto Enegy is stoed in E and B - fields : Enegy volume u = 1 2 E 2 o + 1 B 2 2μ o Use E = cb u = 1 2 E 2 o + 1 E 2 2μ o c = E 2 o E 2 o enegy stoed in E - field = enegy stoed in B - field. enegy Enegy intensity = aea * time = enegy * wave speed = uc volume = o E 2 c = o EBc 2 = EB μ o This enegy flows in the diection given by E B, hence define a enegy flow vecto (called Poynting vecto) S 1 E B μ o

12 Numeical example. An electomagnetic wave popagates in the negative x-diection, its wavelength is 10.6x10-6 m, the electic field is along the z-diection with maximum E-field=1.5x10 6 V/m. Find the instantaneous enegy density, the time aveage enegy density. Find the instantaneous Poynting vecto, the time aveage intensity.

13 Electomagnetic wave also caies momentum - Sola sail

14 Standing EM waves inside a conducting cavity Simila to standing waves of a vibating sting. The "allowed"wavelengths ae fixed by the dimension of the cavity. Fo example : Two paallel conducting plates ae sepaated by a distance L apat (in the x - diection.). The allowed wavelengths ae : 1 = 2L, 2 = 2L 2, = 2L 3 3,..., = 2L n n a set of allowed fequencies: f n = c = n c (n =1,2,3,...) n 2L