We call k the wavenumber which is equal to the number of wavelengths in a distance of 2 and has the dimension Wave vector k The solution for the electric field E in Eq(35.17)represents an electromagnetic wave propagating in the z-direction. For a wave propagating in a general direction, we define a wave vector It is easily verified that the electric field E(F, t)=Eo cos(k,x+ky y+k,z-ot) (35.20) is a solution to Eq. (35. 16), where En is a constant vector The dispersion relation corresponding to Eq.(35.18)is obtained by substituting Eq.(35. 20)in Eq.(35.16 which yields k2+k2+k2 We may write the solution, Eq (35. 20), in the following form E(r, t)=Eo cos( where is a position vector. The wave vector k is often referred to simply as the k vector Wavenumbers k The wavenumber k is the magnitude of the wave vector k and is of more fundamental importance in electro- magnetic wave theory than both of the more popular concepts of wavelength A and frequency f. In Fig. 35.1 we illustrate the electromagnetic wave spectrum according to the free space wavenumber k= k,=(/c. The corresponding values of frequency and wavelength are f= ck /2T and 2= 2T/k,. It is useful to define a fundamental unit K such that for free space k=lK, 2T m-I. Thus k, =A K, corresponds to A=l/A m and f=3x 10 A Hz. The photon energy in electronvolts is calculated from ho hck where h= 1.05 x 10-4 Joule sec is Plancks constant divided by 2T and the electron charge is q=1.6x 10- 9C. Thus h@=(2rthcla)k,=1. 26 10° k and k= A K, corresponds to 1.26×10°AeV Defining Terms Electric field: State of a region in which charged bodies are subject to forces by virtue of their charge, the force acting on a unit positive charge. Magnetic field: State produced by electric charge in motion and evidenced by a force exerted on a moving charge in the field. Magnetic flux: Summation obtained by integrating flux density over an area Magnetic flux density: Measure of the strength and direction of a magnetic field at a point. c 2000 by CRC Press LLC© 2000 by CRC Press LLC We call k the wavenumber which is equal to the number of wavelengths in a distance of 2p and has the dimension inverse length. Wave Vector k The solution for the electric field in Eq. (35.17) represents an electromagnetic wave propagating in the ^ z-direction. For a wave propagating in a general direction, we define a wave vector = ˆ xkx + ˆ yky + ˆzkz (35.19) It is easily verified that the electric field ( ,t) = 0 cos(kx x + ky y + kz z – wt) (35.20) is a solution to Eq. (35.16), where 0 is a constant vector. The dispersion relation corresponding to Eq. (35.18) is obtained by substituting Eq. (35.20) in Eq. (35.16) which yields k 2 x + k 2 y + k 2 z = w2me We may write the solution, Eq. (35.20), in the following form: ( , t) = 0 cos( · – wt) where = ˆ xx + ˆ yy + ˆ xx is a position vector. The wave vector is often referred to simply as the vector. Wavenumbers k The wavenumber k is the magnitude of the wave vector and is of more fundamental importance in electro￾magnetic wave theory than both of the more popular concepts of wavelength l and frequency f. In Fig. 35.1, we illustrate the electromagnetic wave spectrum according to the free space wavenumber k = ko = w/c. The corresponding values of frequency and wavelength are f = ck o /2p and l = 2p/ko . It is useful to define a fundamental unit Ko such that for free space ko = 1Ko = 2p m–1. Thus ko = A Ko corresponds to l = 1/A m and f = 3 ¥ 108 A Hz. The photon energy in electronvolts is calculated from \w = \ck where \ = 1.05 ¥ 10–34 Joule￾sec is Planck’s constant divided by 2p and the electron charge is q = 1.6 ¥ 10–19 C. Thus \w = (2p\c/q)ko ª 1.26 ¥ 10–6 ko and ko = A Ko corresponds to 1.26 ¥ 10–6 A eV. Defining Terms Electric field: State of a region in which charged bodies are subject to forces by virtue of their charge, the force acting on a unit positive charge. Magnetic field: State produced by electric charge in motion and evidenced by a force exerted on a moving charge in the field. Magnetic flux: Summation obtained by integrating flux density over an area. Magnetic flux density: Measure of the strength and direction of a magnetic field at a point. E – k E – r E – E – E – r E – k r r k k k