Energy of an electromagnetic wave

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Discussion Overview

The discussion centers on the relationship between the energy of electromagnetic waves and their frequency and amplitude. Participants explore the implications of the equation E=hf, questioning the role of amplitude in energy calculations and discussing how energy is distributed among photons in different contexts.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant notes that the equation E=hf suggests energy is related solely to frequency, questioning why amplitude does not appear to affect energy.
  • Another participant proposes that higher amplitude corresponds to more photons, implying that energy can be viewed as the sum of energy contributions from multiple photons.
  • A question is raised about the specifics of how photons add up in terms of energy contributions.
  • It is stated that the addition of photons occurs linearly, with ten times as many photons resulting in ten times the energy.
  • A participant inquires about the implications of amplitude being ten times that of one photon, seeking clarification on how this relates to the number of photons.
  • Another participant explains that the energy in an electromagnetic field is proportional to the square of the field strength (amplitude), noting that for coherent light, doubling the amplitude results in quadrupling the energy and the number of photons, while incoherent light behaves differently.

Areas of Agreement / Disagreement

Participants express differing views on the role of amplitude in energy calculations, with some emphasizing the linear relationship with photon count and others introducing the concept of energy being proportional to the square of amplitude in coherent light. The discussion remains unresolved regarding the implications of these differing perspectives.

Contextual Notes

There are limitations in the discussion regarding the definitions of coherent and incoherent light, as well as the assumptions made about energy distribution among photons. The mathematical relationships discussed may depend on specific conditions that are not fully explored.

anorred
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So I've seen this equation used to calculate the energy associated with an electromagnetic wave:

E=hf

E is energy, h is a constant, and f is frequency. Therefore, the energy is related to frequency alone. However, why wouldn't the amplitude of that wave have an effect on the energy? I don't get it. If you have an extremely intense radio wave that requires much more energy to generate than waves such as your cell phone, why doesn't this equation show the effect of amplitude?
 
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Because when you take amplitude into account is like adding E=hf. E is the energy in one "em" wave. So with higher amplitude you are having more photons or "em" wave quanta which adds up.
 
Do you know exactly how they add up?
 
They add linearly. Ten times as many photons is ten times as much energy. Is that what you were asking?
 
Yes, that was what I was asking.. in a way. If you had an amplitude that's 10x the magnitude of one photon.. would you add ten photons? I'm a noob.
 
The energy in an electromagnetic field is proportional to the square of the field strength (amplitude). So for coherent light, doubling the amplitude takes four times the energy and four times the number of photons, all else being equal. The rules for incoherent light are different, doubling the mean amplitude then takes just double the energy, and we use time-average values.
 

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