Electromagnetic Waves in Vacuum

Abstract

Starting from Maxwell’s equations, we want to treat electromagnetic fields that are rapidly alternating in time and space. At first, we will restrict ourselves to fields in vacuum. In this case, D = E and B = H; furthermore, j = 0 and p=O. So, we have Maxwell’s equations in the form

$$ \nabla \times B = \frac{1}{c}\frac{{\partial E}}{{\partial t}} $$

(15.1)

$$ \nabla \times E = - \frac{1}{c}\frac{{\partial B}}{{\partial t}} $$

(15.2)

$$ \nabla \cdot E = 0 $$

(15.3)

$$ \nabla \cdot B = 0 $$

(15.4)