26.6 Maxwell’s equations and electromagnetic waves

Maxwell’s equations describe the behaviour of electric fields and magnetic fields; a more detailed introduction appears in post 25.12. Equations (1)-(4) (highlighted above) are Maxwell’s equations in vector notation. Here E is an electric field, B is a magnetic field, ∇ is the vector operator del, q is charge, ε0 is the permittivity of free space, ∂/∂t denotes partial differentiation with respect to time, μ0 is the permeability of free space and J is current density. Equations (1) and (2) are Gauss’ law in differential form; details are given in post 25.12. Equation (3) is Faraday’s law described as a relationship between fields; details are given in post 25.14. Equation (4) is the differential form of the Maxwell-Ampère law; details are given in post 26.5. Mathematical manipulation of these equations (appendix 1) gives the result that Now I’m going to compare equation 5 with the wave equation (equation 6) from post 19.12. Here ψ is something that varies in space and time, creating a…