Electric field as a function of time

[jasonchiang97]

Homework Statement

Before diving into the quantum-mechanical superposition principle, let’s get some practice with superposition in classical physics. Consider an electromagnetic wave propagating in the z-direction, which is a superposition of two linearly polarized waves. The electric field vector in the wave is E = E_x + E_y, where E_x = a cos(kz − ωt), E_y = b cos(kz − ωt + δ). (1) The parameter δ is a real number between −π/2 and π/2, and indicates by how much the two components are out of phase. Look at the behavior of the electric field at some fixed value of z, say z = 0 for simplicity.

a) [2pt] Describe what the electric fields E_x and E_y are doing as a function of time.

Homework Equations

E = E_x + E_y

The Attempt at a Solution

Well I'm not really sure how to start the problem so I just tried to put it into complex form

E_x = a*e<sup>i(kz-ωt)/SUP]
E_y = b*ei(kz-ωt + δ)

Since they are separate components, I cannot add them together so I am unsure of what to do next</sup>

 

[BvU]

so I just tried to put it into complex form

Making things difficult, eh ? Why do so if you have an expression for $E_x$ and for $E_y$ as a function of $z$ and $t$ and the first part of the exercise asks for $E_x$ and $E_y$ as a function of $t$ for a given $z$ ?

Things may be more complex in part b) but I can't guess and you don't tell ...

 

[jasonchiang97]

Making things difficult, eh ? Why do so if you have an expression for $E_x$ and for $E_y$ as a function of $z$ and $t$ and the first part of the exercise asks for $E_x$ and $E_y$ as a function of $t$ for a given $z$ ?

Things may be more complex in part b) but I can't guess and you don't tell ...

Ah, so I can just set z=0 and I would have my function?

 

[BvU]

Bingo