Question

A plane monochromatic electromagnetic wave with wavelength ? = 3 cm, propagates through a vacuum. Its magnetic field is described by

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

where Bx = 3.3 X 10-6 T, By = 3.9 X 10-6 T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively.

1)

What is f, the frequency of this wave?

GHz

2)

What is I, the intensity of this wave?

W/m2

3)

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

W/m2

4)

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

V/m

5)

Compare the sign and magnitude of Sz, the z-component of the Poynting vector at (x=y=z=t=0) of the wave described above to the sign and magnitude of SIIz, the z-component of the Poynting vector at (x=y=z=t=0) of another plane monochromatic electromagnetic wave propagating through vaccum described by:

B? =(BIIxi^?BIIyj^)cos(kz??t)

where BIIx = 3.9 X 10-6 T, BIIy = 3.3 X 10-6 T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively.

SIIz < 0 and magnitude(SIIz) =/ (does not equal sign) magnitude(Sz)

SIIz < 0 and magnitude(SIIz) = magnitude(Sz)

SIIz > 0 and magnitude(SIIz) =/ (does not equal sign) magnitude(Sz)

SIIz > 0 and magnitude(SIIz) = magnitude(

Answer 1

Answer:The Poynting vector SS represents the flow of energy in an EM field. Specifically, if uu is the energy density of the field, the Poynting vector satisfies the continuity equation for it:

∂u∂t+∇⋅S=0

∂u∂t+∇⋅S=0

in vacuum. (This is Poynting's theorem.)

In your particular problem, EE and BB are perpendicular and their cross product is proportional to the product of their amplitudes. Thus

Sz=cμ0B2.

Sz=cμ0B2.

You then have to use your knowledge of BB to work out SS.

Explanation: