PHYS 2212 Module 12.2

Plane Electromagnetic Waves

Recommended Reading

12.2 Plane Electromagnetic Waves

Learning Objectives

By the end of this section, you will be able to:

  • Describe how Maxwell’s equations predict the relative directions of the electric fields and magnetic fields, and the direction of propagation of plane electromagnetic waves
  • Explain how Maxwell’s equations predict that the speed of propagation of electromagnetic waves in free space is exactly the speed of light
  • Calculate the relative magnitude of the electric and magnetic fields in an electromagnetic plane wave
  • Describe how electromagnetic waves are produced and detected

Producing EM Waves with a Dipole Antenna

Electromagnetic Waves (EM waves) are waves consisting of oscillating electric and magnetic fields. These EM waves are produced by accelerating charges, like electrons speeding up, slowing down, or changing direction. Consider something called a dipole antenna – this is simply a wire that has an alternating (AC) current in it so that one end of the wire is positive and the other end is negative, like an electric dipole. As the electrons move in this dipole antenna,

  • The charges are always accelerating (since the velocity is always changing)
  • These accelerating charged particles emit E-fields
  • These moving charged particles (current) emit B-fields
  • Changing B-fields induce E-fields (Faraday’s law)
  • It turns out that changing E-fields induce B-fields, too (another law we didn’t discuss – too much calculus required)

So: E-field → ΔB-field → ΔE-field → ΔB-field → ΔE-field → etc…

A changing B-field → E-field and a changing E-field → B-field →→→ Each field is a source for the other

There are no electric waves or magnetic waves, there are only electromagnetic waves.


Practice 12.2.1
At a certain point in space, the electric and magnetic fields of an electromagnetic wave at a certain instant are given by:

This wave is propagating in the…
Check your answer: D. negative y-direction.
Practice 12.2.2
Consider an electromagnetic wave traveling in the positive y direction. The magnetic field associated with the wave at some location at some instant points in the negative x direction as shown in the figure below.

What is the direction of the electric field at this position and at this instant?
Check your answer: F. negative z direction