Question

Write the plane wave form for the z-component of the electric field vector of an electromagnetic wave of wavelength 10 cm and field strength 200 Vm^–1. The wave is propagating in the positive x-direction

Answer 1

General equation of an electromagnetic wave plane wave

$$E_z(x,t)=E_0 \exp\left[i(\omega t-kx)\right]$$

The wave number

$$k=\frac{2\pi}{\lambda}=\frac{2\pi}{0.1}=20\pi\;\rm{m^{-1}}$$

The frequency

$$\omega=ck=3\times 10^{8}\:\rm{m/s}\times 20\pi\;\rm{m^{-1}}=6\pi\times 10^{9}\;\rm{s^{-1}}$$

Finally

$$E_z(x,t)=200 \exp\left[i(6\pi\times 10^{9} t-20\pi x)\right]\:\rm{V/m}$$