Deriving the Wave Equation from Maxwell's Eqns

Deriving the Wave Equation from Maxwell's Eqns.

Splitting the flux f into area • field intensity and taking the partial derivative of both sides:

To find the wave equation for E:

Similarly for B:

Traveling Electromagnetic Waves

E = Em sin (kx-wt) & B = Bm sin (kx-wt)

From before:

kEm cos (kx - wt) = wBm cos (kx - wt) Þ

Where c is the wave speed for light:

c = 299,792,458 m/s (by definition)

Energy Transport and The Poynting Vector

(the Poynting Vector)

•S has units of Watts/meter

•And since

(instantaneous energy)

•But the average energy flow is:

The radiation pressure is:

where U is the energy delivered

and p is the momentum