traveling wave Wave equation law of induction 34

電磁波的數學特性 • traveling wave(一維) • 滿足的微分方程式 – Wave equation law of induction – (34 -11) ←由Faraday’s eq. 34 -6, 32 -26 – (34 -17) ←由Maxwell’s law of induction eq. 34 -11, 32 -27 Wave eq.

例題Ch 34 -102(a)(b) 102. A plane electromagnetic wave with a wavelength of 200 nm is traveling in a vacuum in the positive x direction. Its magnetic field, whose maximum magnitude is 50 μT, is polarized parallel to the z axis. (a) Write the wave velocity as a vector. (b) Determine the following characteristics of the wave: its frequency f, its angular frequency ω, and its angular wave number k. What part of the electromagnetic spectrum is involved? λ=200 μm 屬於紫外光（可見光是 400~700 um）

例題Ch 34 -102(c)(d) (c) Write a mathematical expression for the magnetic field of this wave. Take the phase constant to be zero, and remember that the magnetic field is a vector. (d) Similarly, write an expression for the electric field vector of this wave.

例題Ch 34 -102(e) Faraday’s law applied to the electric and magnetic fields of a plane electromagnetic wave leads to the relation (Eq. 34 -11, written in component notation). Verify that this equation is satisfied by the magnetic and electric fields derived parts (c) and (d). 代入

例題Ch 34 -102(f) From his four electromagnetic equations, Maxwell derived the wave equations for electromagnetic waves as and Verify that the electric field in this problem satisfies the wave equation for.