Electromagnetic Wave Incident on a Perfect Conductor

This Demonstration shows an electromagnetic wave incident on a perfect conductor calculates the corresponding Poynting vector. The incident wave is assumed to be linearly polarized in the horizontal or vertical direction (with respect to the electric field). The resulting Poynting vector pattern is shown on the incident - plane. In all cases, the amplitude of the incident electric field is set to , which corresponds to or in power density.
The Poynting vector is calculated using , where and are the electric and magnetic fields. The fields can be calculated by superposing the fields for the incident and reflected waves. You can show the individual Poynting vectors of the incident wave, the reflected wave, or their superposition.
You can set the frequency in the range 0.1–1.0 GHz and the incident angle at 0–90°. The phase of the sinusoidal cycle can be changed, but this results in time-consuming computations.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Snapshot 1: Poynting vector plot for vertically polarized incident wave at angle
Snapshot 2: Poynting vector plot for incident wave of (same for horizontal or vertical waves)
Snapshot 3: Poynting vector plot for reflected wave for incident wave of (same for horizontal or vertical waves)
For the horizontally-polarized electromagnetic wave propagating along the axis, the electric field is given by , while for the vertically-polarized wave, . Here, is the propagation factor. In both cases, the corresponding magnetic field is given by , where is the propagation direction, and is the wave impedance.
Similarly, the fields for the incident angle can be determined for both incident reflected waves as . Then the resultant fields and can be obtained by superposition. The Poynting vector can be calculated accordingly.
The Poynting vector pattern of the incident wave (or reflected wave) is the same whether the polarization is horizontal or vertical. However, the superposed pattern is different because the reflected wave's phase depends on the polarization.
The Poynting vector's intensity and direction are shown by colors and arrows in the output pattern. The intensity increases as approaches 90°, and the average direction is always toward the positive direction.
[1] D. K. Cheng, Field and Wave Electromagnetics, 2nd ed., Reading, MA: Addison-Wesley, 1989.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+