a right- moving EM wave overlaps with a left-moving wave so in a certain region

Question

a right- moving EM wave overlaps with a left-moving wave so in a certain region of space the total electric field in the y-direction and the magnetic field in the z direction are give: Ey = E0 sin(kx-wt) + E0 sin (kx+wt) Bz = B0 sin(kx-wt)+ B0 sin (kx+wt) a. find the mathematical expression that represents the standing electric and magnetic waves in the y and z direction respectively ( use trig identity). b. What would be the amplitude ( as function of x) of each of these resulting E and B fields? c. Determine the Poynting Vector and find the x-location at which it is zero at all times.

Explanation / Answer

Ey = E0 sin(kx-wt) + E0 sin (kx+wt)

==> Ey = E0 (sin(kx-wt) + sin (kx+wt))

==> Ey = E0 cos(wt) sin(kx)

Bz = B0 sin(kx-wt)+ B0 sin (kx+wt)

==> Bz = B0 cos(wt) sin(kx)

b)

E field:

E0 sin(kx)

B field:

B0 sin(kx)

c)

S = 1/u0 (E x B) = (1/u0) ((E0 cos(wt) sin(kx)) x (B0 cos(wt) sin(kx)))

==> S = ((E0 B0)/(u0)) (cos(wt) sin(kx))^2

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