An electromagnetic wave traveling in a vacuum is linearly polarized and sinusoid

Question

An electromagnetic wave traveling in a vacuum is linearly polarized and sinusoidal in form. The electromagnetic wave is traveling in the positive x direction. The wavelength of the wave is 5.10 mm. The magnetic field of the wave oscillates in the xz plane and has an amplitude of 8.60 µT. The magnitude of the electric field vector for this wave can be written as

E = Emax sin(kx t).

Find the following.

(a) the value of Emax
V/m

(b) the wave number k
m1

(c) the angular frequency
rad/s

(d) the plane in which the electric field oscillates

the xz planethe yz plane    the xy plane

(e) the average Poynting vector (Express your answer in vector form.)

Explanation / Answer

Bmax = 8.6 uT

(a) Emax = Bmax*c

= 8.6*10^-6*3*10^8 = 2580 V/m

(b) lamda = 5.1 mm

k = 2pi/lamda

k = 2*3.14/0.0051

k = 1231.4 rad/m

(c) w/k = c

w = 3*10^8*1231.4

w = 3.7*10^11 rad/s

(d) in electromagneitc wave electric and magnetic ileds are perpendicular to each other.

yz plane

(e) Sav = 0.5eoE^2*c

sav = 0.5*8.85*10^-12*2580^2*3*10^8

sav = 8836.4 i W/m^2

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