Over what frequency range are Maxwell's equations valid?

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Homework Help Overview

The discussion revolves around the validity of Maxwell's equations across different frequency ranges, particularly in the context of an optics exam. Participants are exploring the implications of these equations in relation to frequency and potential limitations, especially concerning quantum mechanics.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants express uncertainty about the frequency dependence of Maxwell's equations and question whether they are valid at all frequencies. Some mention the potential relevance of quantum electrodynamics (QED) and discuss the level of the question in relation to undergraduate optics.

Discussion Status

The discussion is ongoing, with various interpretations being explored. Some participants suggest that the question may be basic, while others consider the implications of quantum mechanics. There is no explicit consensus on the frequency limitations of Maxwell's equations, and participants are seeking further insights.

Contextual Notes

Some participants note that the question is not for a formal class and mention their familiarity with differential equations and Maxwell's equations. There is a recognition that the level of the exam may influence the expected depth of understanding regarding frequency limitations.

MathPi
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Homework Statement


I am studying for an Optics exam and in one of the practise tests is the following question: "Over what frequency range are Maxwell's equations valid?"

Homework Equations


Maxwell's Equations

The Attempt at a Solution


I've searched through my Griffiths Intro to electrodynamics, and all over Google, but came out short. Any leads would be appreciated.
 
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MathPi said:

Homework Statement


I am studying for an Optics exam and in one of the practise tests is the following question: "Over what frequency range are Maxwell's equations valid?"

Homework Equations


Maxwell's Equations

The Attempt at a Solution


I've searched through my Griffiths Intro to electrodynamics, and all over Google, but came out short. Any leads would be appreciated.
Do you see any frequency dependent terms in Maxwell's Equations? Are you familiar with how to work with differential equations like the linked system of Maxwell's Equations?

https://upload.wikimedia.org/wikipe...quations.svg/500px-Maxwell'sEquations.svg.png
500px-Maxwell'sEquations.svg.png
 
MathPi said:

Homework Statement


I am studying for an Optics exam and in one of the practise tests is the following question: "Over what frequency range are Maxwell's equations valid?"

Homework Equations


Maxwell's Equations

The Attempt at a Solution


I've searched through my Griffiths Intro to electrodynamics, and all over Google, but came out short. Any leads would be appreciated.

I should add that this is not homework for a class that I am taking, nor am I receiving any marks for answering this question.
berkeman said:
Do you see any frequency dependent terms in Maxwell's Equations? Are you familiar with how to work with differential equations like the linked system of Maxwell's Equations?

https://upload.wikimedia.org/wikipe...quations.svg/500px-Maxwell'sEquations.svg.png
500px-Maxwell'sEquations.svg.png
Yes I am familiar with solving DEs (I have a math degree). I am also familiar with Maxwells equations (I also have a physics degree). The question is literally as I have posted it - my best guess is that the these laws are not good at the quantum level and QED must be used (I am not too good at QED, I only took one course in subatomic physics).

I should add that this is not a homework question for a course I am taking. Nor am I receiving any marks for answering this.
 
MathPi said:
"Over what frequency range are Maxwell's equations valid?"
MathPi said:
my best guess is that the these laws are not good at the quantum level and QED must be used (I am not too good at QED, I only took one course in subatomic physics).
How are these two statements related? Your OP said nothing about QM, only about frequency limitations...
 
berkeman said:
How are these two statements related? Your OP said nothing about QM, only about frequency limitations...
It's just a guess - trying to come to an answer through discussion. Any constructive input is appreciated :)
 
I think you are over-thinking it.
berkeman said:
Do you see any frequency dependent terms in Maxwell's Equations?
What level is this question anyway. From your OP it sounded like it was at a pretty basic level:
MathPi said:
I am studying for an Optics exam
Opticians don't do much with QM.

OTOH, if this is for a Quantum Optics class, there may be a different answer, I suppose.
 
berkeman said:
I think you are over-thinking it.

What level is this question anyway. From your OP it sounded like it was at a pretty basic level:

Opticians don't do much with QM.

OTOH, if this is for a Quantum Optics class, there may be a different answer, I suppose.
Ah I should have specified the level. The exam is for an undergraduate optics at an advanced EM level (maybe 4th year physics).
 
MathPi said:
Ah I should have specified the level. The exam is for an undergraduate optics at an advanced EM level (maybe 4th year physics).

Even if I am overthinking it there are only two possibilities: either Maxwells equations are valid for all frequencies, or they are not. If not, what are the ranges and why?
 
So QED may be involved? I'm not familiar with any frequency limitations of Maxwell's Equations, but are they modified for QED? That's kind of a different question.
 
  • #10
berkeman said:
So QED may be involved? I'm not familiar with any frequency limitations of Maxwell's Equations, but are they modified for QED? That's kind of a different question.
I doubt QED is involved - that's too advanced for this course. Like I said it was just a guess - maybe not a good one! I cannot think of anything else besides that (trying to remember my subatomic physics course).
 
  • #11
At least from my perspective, frequency limitations do not come into effect with the basic Maxwell Equations. Probably a trick question...
 
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  • #12
berkeman said:
At least from my perspective, frequency limitations do not come into effect with the basic Maxwell Equations. Probably a trick question...
Yes you might be right. Perhaps I was hoping there was more to it. I'll take it as it is for now unless someone else has any thoughts. Thanks for your input!
 
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