How do I modify plane waves to represent the EM field of a lightbulb?

[e101101]

Homework Statement

Part c

Relevant Equations

B=Bocos(k•r±⍵t)
E=Eocos(k•r±⍵t)
Irradiance=P/A

I don't know where to start for part (c), I've managed to get (a) and (b).
Can someone simply guide me, I think I'm having trouble understanding what the teacher means by just having an x dependance...
Does this mean I only work with the x components of the magnetic field and the electric field? What about the direction fo propagation?

 

[collinsmark]

Homework Statement: Part c
Homework Equations: B=Bocos(k•r±⍵t)
E=Eocos(k•r±⍵t)
Irradiance=P/A

I don't know where to start for part (c), I've managed to get (a) and (b).

What is the relationship between irradiance*, $I$, and the electric field amplitude (by that I mean the electric field amplitude is the $E_0$ in your $E = E_0 \cos(kr \pm \omega t)$ equation [Note: that equation, as it stands, doesn't apply to this problem. You'll have to modify it a little to apply to this problem])?

In this problem, the irradiance is a function of distance from the light source. What is the relationship between irradiance and distance, in this problem?

Now, based on the above, what is the relationship between the electric field amplitude and distance from the light source?

*(here I'm assuming that "irradiance" is synonymous with "intensity.")

Can someone simply guide me, I think I'm having trouble understanding what the teacher means by just having an x dependance...
Does this mean I only work with the x components of the magnetic field and the electric field? What about the direction fo propagation?

I'm pretty sure it just means that you don't need to worry about forming equations in 3-dimensions for all space. Just concentrate on a single direction (specifically, that direction being the x-axis).

The direction of propagation is the x-axis. So all you need to do is determine $E$ and $B$ as measured along the x-axis.

 

[collinsmark]

Also, I don't think the problem is asking for the actual directions of the electric and magnetic field vectors. It's assumed that $\vec E$ and $\vec B$ are perpendicular to each other, and both are perpendicular to the direction of wave propagation.

Rather, I think the problem is just asking you to find the magnitudes of $E$ and $B$, as a function of distance from the light source.

 

[e101101]

What is the relationship between irradiance*, $I$, and the electric field amplitude (by that I mean the electric field amplitude is the $E_0$ in your $E = E_0 \cos(kr \pm \omega t)$ equation [Note: that equation, as it stands, doesn't apply to this problem. You'll have to modify it a little to apply to this problem])?

In this problem, the irradiance is a function of distance from the light source. What is the relationship between irradiance and distance, in this problem?

Now, based on the above, what is the relationship between the electric field amplitude and distance from the light source?

*(here I'm assuming that "irradiance" is synonymous with "intensity.")I'm pretty sure it just means that you don't need to worry about forming equations in 3-dimensions for all space. Just concentrate on a single direction (specifically, that direction being the x-axis).

The direction of propagation is the x-axis. So all you need to do is determine $E$ and $B$ as measured along the x-axis.

Thank you so much for your reply!
Would I have to consider spherical waves in this problem? Or can I simply treat them as plane waves moving in the x direction (because of the conditions given in the problem).

If I can treat it as a planar wave i would write an equation like:
Ex=Eo(kx±⍵t)

The relationship between irradiance and the amplitudes would be: (1/μ0)(BoEo)
and since Bo=Eo/c
we can rewrite as (1/μ0)(Eo**2)/c

 

[collinsmark]

Thank you so much for your reply!
Would I have to consider spherical waves in this problem? Or can I simply treat them as plane waves moving in the x direction (because of the conditions given in the problem).

If I can treat it as a planar wave i would write an equation like:
Ex=Eo(kx±⍵t)

The relationship between irradiance and the amplitudes would be: (1/μ0)(BoEo)
and since Bo=Eo/c
we can rewrite as (1/μ0)(Eo**2)/c

Your final answers will be something sort of like plane waves, but not exactly like plane waves. In other words, modify your

$E = E_0 \cos (kr \pm \omega t)$
$B = B_0 \cos (kr \pm \omega t)$

equations such that the (a) amplitude falls off appropriately as a function of distance and (b) instead of using the constants $E_0$ and $B_0$ use some other expressions that relate to a 80 W light bulb at 50% efficiency.