Waves and Vectors

A.2.1 Waves and Vectors

This is generally the way that, for example, water waves are considered, with high and low troughs in the water. Similarly electromagnetic waves can be modelled in this way, where the oscillation occurs in the electric field. The magnetic field associated with the electric field also oscillates, but is π/2 out of phase with the electric field. Consequently if the electric field is described by a cosine wave, the magnetic field will be executing a sine oscillation. This is shown in Fig. 2.2.

Note that we are now describing two oscillating components that are a sine and cosine function. Mathematically, this can therefore be simplified by using a vector in imaginary space that rotates between the real and imaginary axes along the length of the wave (shown in the right hand panel of Fig. 2.2). It is, therefore much more convenient to use a modulus argument form of the wave, as it will allow us to consider all waves in a vector form. 

Figure 2.2: The Vector Model of Electromagnetic Radiation