An electromagnetic plane wave with an irradiance of 120 W/m^2 has its electric f

Question

An electromagnetic plane wave with an irradiance of 120 W/m^2 has its electric field in the z direction at some time and travels in empty space in the x direction. It has a wavelength of 500 nm.

a) What is the direction of the magnetic field?

b) What is the magnitude of the electric field?

c) Write an expression for the electric field as a function of position and time.

d) If we observed the same irradiance for a spherical wave from a point source 50m away emitting isotropically what would the total power emitted by the point source be?

Explanation / Answer

In em wave, always EF, mag field will be perpendicular to each and in turn perpendicular to propagation of the wave

since E is in z direction and sppped is in x directon

magnetic field must be a long y axis
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b. Apply I = ppower/area = Emax^2/2uoC

so Emax^2 = I *2 uoC/

Emax^2 = 120 * 2* 4pie-7 *3e8

Emax^2 = 90432

Emax = 300.71 V/m or N/C
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Emax = Eo cos(Kx-wt)

here K = 2pi/L = 6.28/500e-9   = 1.256 *10^7

as V = Lf

f = 3e8/500nm = 6e14

W = 2pif   = 2*3.14* 6e14 = 3.768 e15 rad/s

si expression is E = Eo cos (1.256e7 x - 3.768 e5 t)
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power = IA

P = 120 * 4pi * 50*50

P = 3.768 *10^6 Watts

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