An electromagnetic wave
Here is a particular electromagnetic field in free space:
E_x = 0, E_y = E_0 sin(kx + ωt), E_z = 0; (9.64)
B_x = 0, B_y = 0, B_z = −(E_0/c) sin(kx + ωt).
464 Maxwell's equations and EM waves
(a) Show that this field can satisfy Maxwell's equations if ω and k are related in a certain way.
(b) Suppose ω = 10^10 s^−1 and E_0 = 1 kV/m. What is the wavelength? What is the energy density in joules per cubic meter, averaged over a large region? From this calculate the power density, the energy flow in joules per square meter per second.