Intensity of Electromagnetic Waves

[diethaltao]

Homework Statement

A plane monochromatic electromagnetic wave with wavelength λ = 2.2 cm, propagates through a vacuum. Its magnetic field is described by
\vec{B} = (Bx\vec{i} + By\vec{j})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?

 

[vela]

You need to understand what the symbols in the various formulas you have represent. In the expression for the intensity $I$, $E$ is the amplitude of the electric field wave, what you later called $E_0$. You can find $B_0$ from the expression for $\vec B$ and then use $E_0 = cB_0$ to find the electric field amplitude to plug into the intensity formula.

 

[Delta2]

In addition to what @vela said, you might find also rather obvious to use pythagorean theorem to find $B_0$ , $$B_0=\sqrt{B_x^2+B_y^2}$$