Electromagnetic Waves Electromagnetic waves are identical to mechanical waves with the exception that they do not require a medium for transmission. The “medium” is the electric and magnetic fields that travel with the wave. The electric and magnetic fields are oscillating in time. What does an oscillating magnetic field cause? What does an oscillating electric field cause? An oscillating electric field. An oscillating magnetic field. This can all be described using Maxwell’s Equations The oscillating electric field and the oscillating magnetic field are always perpendicular to each other. They are also perpendicular to the direction of propagation of the wave.

We describe the motion (propagation and oscillation) of a wave using the wave equation. We will look at the wave equation for a plane electromagnetic wave. Plane wave – All waves from a single source are traveling in a single direction and all of the corresponding oscillations occur in a single plane perpendicular to the direction of propagation. Assumptions: 1) All waves are in phase. 2) All rays are parallel. 3) E and B are only functions of x and t. 4) E is in y-direction and B is in z- direction. 5) We are in empty space q = 0 and I = 0. Ray – line along which a wave propagates. 0 The derivation of these equations is presented in the text, but will not be discussed here. We can now relate the electric field and the magnetic field. We want a single expression that includes either the magnetic field or the electric field. We can do this by first differentiating either of the two expressions shown with respect to x.

Similarly for B: Generalized Wave Equation: Define c in order to have a similar form. We can then obtain a solution to these second order differential equations. x – location along x-axis t – time w – angular frequency of oscillation k – angular wave number Wave speed equation

Now that we have determined the solutions to the differential equation describing the oscillations of the electric and magnetic fields with respect to time and position, we can determine a relationship between E and B. We can do this by substituting the solutions into one of the following equations. We will use the second equation since it is simpler. The ratio of the magnitude of the electric field to the magnitude of the magnetic field is a constant, specifically the speed of light!

The speed of light is a constant because the electric and magnetic fields support each other. If the speed of light was not constant energy would not be conserved!! Remember: Electromagnetic waves are a means of transmitting energy. The rate at which the energy is being transmitted is defined in terms of the Poynting Vector. S – Poynting Vector [W/m 2 ] For plane waves: We can also determine the intensity of the light from the magnitudes of the electric and magnetic fields. The factor of ½ is from the time average of the sinusoidally varying function that describes E and B in terms of position and time. If c increases in time spontaneously gain energy. If c decreases in time spontaneously lose energy.