- #1

diethaltao

- 14

- 0

## Homework Statement

A plane monochromatic electromagnetic wave with wavelength λ = 2.2 cm, propagates through a vacuum. Its magnetic field is described by

[itex]\vec{B}[/itex] = (Bx[itex]\vec{i}[/itex] + By[itex]\vec{j}[/itex])cos(kz+ωt)

where Bx = 1.8E-6 T and By = 3.8E-6 T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively.

What is I, the intensity of this wave?

## Homework Equations

I = P/A = (1/2)cεoE^2

k = (2π)/λ

ω = ck

Bo*c = Eo

## The Attempt at a Solution

I found frequency to be c/λ = 13.63GHz.

I have tried setting t to zero in the given equation and plugging in k and ω to find B, then multiplying that by the speed of light to find E.

I then plugged that into I = (1/2)cεoE^2, but that gave me the wrong answer.

I've also tried adding to the two vectors and assumed that equaled Bo (which I don't think it does), and used Bo = (√2ZoI)/c where Zo = 377 ohms.

I've tried <B^2> = (Bo^2)/2 as well.

Is there an important equation I'm missing?