Electromagnetic Waves 2 1 2 3 4 1 6 A plane monochromatic electromagnetic wave w

ID: 1612288 • Letter: E

Question

Electromagnetic Waves 2

A plane monochromatic electromagnetic wave with wavelength = 4.4 cm, propagates through a vacuum. Its magnetic field is described by

B =(Bxi^+Byj^)cos(kz+t)B=(Bxi^+Byj^)cos(kz+t)

where Bx = 2.4 X 10-6 T, By = 4.1 X 10-6 T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively.

What is f, the frequency of this wave?

GHz

What is I, the intensity of this wave?

W/m2

What is Sz, the z-component of the Poynting vector at (x = 0, y = 0, z = 0) at t = 0?

W/m2

What is Ex, the x-component of the electric field at (x = 0, y = 0, z = 0) at t = 0?

V/m

lamda = 4.4 cm

c = 3*10^8 m/s

c = f*lamda

3*10^8 = f*0.044

f = 6.82*10^9 Hz

(b) I = B^2c/(2uo)

B = 10^-6(2.4^2 +4.1^2)^0.5

B = 4.75*10^-6 T

I = 0.5*(4.75*10^-6)^2*3*10^8/(4*3.14*10^-7)

I = 2694.6 W/m^2

c) S = ExB

Sz = ceo(Boc)^2

= 3*10^8*8.85*10^-12(4.75*10^-6*3*10^8)^2

Sz = 5391 W/m^2

(d)

Ex = Eo(cos(theta))

theta = arctanBy/Bx)

theta = arctan(4.1/2.4) = 59.66 degrees

Ex = (Boc)cos(59.66)

Ex = (4.75*10^-6*3*10^8)cos(59.66)

Ex = 720 V/m

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