lecture 6

Lecture 6
Maxwell’s wave equation in vacuum
The wave equation in vacuum is the simplest form of this equation (why?). The derivation of the electromagnetic wave equation in vacuum demonstrates that this kind of wave needs no medium for its existence.
In vacuum Maxwell’s equations can be reduced to:
??E=0 or ??D=0 ……… (17)
??H=0 or ??B=0 ……… (18)
?×H=?_o ?E/?t ………… (19)
?×E=?-??_o ?H/?t ………… (20)
(Why?)
By tacking the curl of eq. (20) and using eq. (19) one gets:
?^2 E=?_o ?_o (?^2 E)/(?t^2 ) ……… (21)
where ?×?×E=?(??E)-?^2 E, and the first term is cancelled in the case of free space according to eq. (17). (How?)
A similar form can be obtained for the magnetic field from Maxwell’s equations, (Prove it).

Maxwell’s wave equation in vacuum
The wave equation in vacuum is the simplest form of this equation (why?). The derivation of the electromagnetic wave equation in vacuum demonstrates that this kind of wave needs no medium for its existence.
In vacuum Maxwell’s equations can be reduced to:
??E=0 or ??D=0 ……… (17)
??H=0 or ??B=0 ……… (18)
?×H=?_o ?E/?t ………… (19)
?×E=?-??_o ?H/?t ………… (20)
(Why?)
By tacking the curl of eq. (20) and using eq. (19) one gets:
?^2 E=?_o ?_o (?^2 E)/(?t^2 ) ……… (21)
where ?×?×E=?(??E)-?^2 E, and the first term is cancelled in the case of free space according to eq. (17). (How?)
A similar form can be obtained for the magnetic field from Maxwell’s equations, (Prove it).