- #1

rogeralms

- 19

- 0

## Homework Statement

Consider a harmonic, electromagnetic plane wave traveling along a line from the origin to the point (3,5,6). It is linearly polarized and its electric field lies in a plane perpendicular to the direction of travel of the wave. The wavelength of the wave is 2.0mm and it has a frequency of 100 GHz.

a) Write an expression for the magnitude (i.e. don't worry about the orientation) of the electric field of this plane wave if the amplitude of the electric field is 10V/m.

b) What is the index of refraction of the medium in which the wave is traveling?

c) Compute the irradiance of the wave.

d) Determine a unit vector for a possible direction that would define the direction of the electric field.

## Homework Equations

**k**= 3

**i**+ 5

**j**+ 6

**k**

|k| = (3

^{2}+ 5

^{2}+ 6

^{2})

^{(1/2)}

unit vector in k direction =

**k**/ (70)

^{(1/2)}

n= v/c

**E**(dot)

**k**= 0

I = (c * epsilonzero /2) * (E

_{0})

^{2}

## The Attempt at a Solution

a) I am really confused as to how to find the magnitude of the electric field

As you see, I have the magnitude of the direction vector

**k**.

I know that the divergence of the

**E**and

**k**vectors is zero. But I don't know how the amplitude is used in the magnitude. Please I do not want the final answer, just a reference as to how to find the magnitude.

b) v = lambda * nu = 2*10

^{-3}* 100*10

^{9}= 2*10

^{8}m/s

n = c/v = 3*10

^{8}/ 2*10

^{8}= 1.5

c) I = (c*ep

_{0}/ 2)* E

_{0}

^{2}=

150 ep

_{0}*10

^{8}V/m

d) I'm not sure on this one

It has something to do with divergence of

**E**

**k**= 0

Would it be something like

(3-x)E

_{x}+ (5-y)E

_{y}+ (6-z)E

_{z}= 0?

Thanks for any help. I just need some hints.