Answer to Question #93503 in Electricity and Magnetism for MGM

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

Angular frequency:

$$\omega=2\pi \frac{c}{\lambda}$$

Propagation constant:

$$k= \frac{2\pi}{\lambda}$$

$$E_z=200\sin{(\frac{2\pi}{\lambda}x-2\pi \frac{c}{\lambda}t)}$$

$$E_z=200\sin{(\frac{2\pi}{0.1}x-2\pi \frac{3\cdot 10^8}{0.1}t)}$$

$$E_z=200\sin{(62.8x-1.88\cdot 10^{10}t)} \frac{V}{m}$$