Generating A Plane Wave

Generating A Plane Electromagnetic Wave

This applet presents the electric and magnetic fields of a moving sheet of positive charge. You can move the positive charges in that sheet by clicking somewhere in the red rectangle and dragging up and down. This motion of the charges will generate an electromagnetic wave.

After you have clicked on the red rectangle, as long as you are dragging the mouse, time will move forward and the wave will propagate. As soon as you stop dragging the mouse, time freezes at that instant, and the wave stops propagating. This then gives you a snapshot of the wave you have generated up to that point, so that you can analyze what was generated at your leisure. If you want to increase the speed of light (in arbitrary units), use the scroll bar at the bottom. When you increase this parameter, is the resultant change in the waveform what you expect?

What Is Going On

The motion of the positive charges generates a wave in the electric field, since that field is rooted in the charges. We have also put in this applet the field of a negatively charged sheet which has the same magnitude of charge per unit area, but which is always at rest. The presence of this negative sheet of charge cancels out the field of the positive sheet of charge, except for that component of the field parallel to the sheet. This is how you generate a transverse electromagnetic plane wave with the electric field in the plane of the screen and the magnetic field out of the plane of the screen.

At the top of the applet we show the electric field due to the positively charged sheet, which is the sheet that you move up and down when you move the mouse. This up and down motion puts a wave in that electric field which propagates away from the sheet at the speed of light. We also show at the top the electric field due to the negatively charged sheet, which is always at rest. The sum of this field and the field of the moving positively charged sheet give the total field outside of the sheet. The component of the electric field perpendicular to the sheet cancels, but the component of the electric field parallel to the sheet does not. We are left with only that parallel component of the electric field outside of the sheet.

At the bottom of the applet we show that parallel component of the electric field. We also show the magnetic field that is generated by moving the positively charged sheet. Note the sense of this magnetic field is right-handed with respect to the charge motion of the sheet at the time it was generated (the magnetic field subsequently propagates away from the sheet at the speed of light).

For more on the physics and mathematics of what is going on here at a freshman level, see the pdf document at this link which was handed out in class on November 22. If you are really fascinated by this and have the mathematics background, you might want to look at this at junior/senior level at this link, which are notes from 8.07.