A plane monochromatic electromagnetic wave with wavelength ? = 3.9 cm, propagate

Question

A plane monochromatic electromagnetic wave with wavelength ? = 3.9 cm, propagates through a vacuum. Its magnetic field is described by
B=(Bxi^+Byj^)cos(kz+?t)

where Bx = 1.7 X 10-6 T, By = 5.9 X 10-6 T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively.

2) What is I, the intensity of this wave?

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

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

Explanation / Answer

1. k = 2pi / wavelength. Do the calculation.
2. Maximum Z value is done by evaluating the B expression. What will make sin(kz-wt) equal to 1?
t is 0, so kz is the thing you are interested in. You found k in number one, find z.
3. Emax is E0*sqr(2). E0 is simply B1*C, where c is the speed of light.
4. Ey is B1*C, but you find out it is in the negative direction.

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