How Is the Energy Density of EM Waves Related to Capacitors and Inductors?

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Discussion Overview

The discussion centers on the relationship between the energy density of electromagnetic (EM) waves and the energy densities associated with capacitors and inductors. Participants explore theoretical underpinnings, including references to Poynting's theorem and Maxwell's equations, while questioning the validity of deriving energy density in this context.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant states that the energy density of an EM wave is given by the formula (1/2) ϵ E^2 + (1/(2μ)) B^2, derived from capacitors and inductors.
  • Another participant challenges this derivation, suggesting that textbooks may only assume this relationship without proper derivation.
  • A participant references Poynting's theorem as a key concept relevant to the discussion.
  • Some participants assert that the Energy Conservation law applies, indicating that passive components in a transmitter must pass on the same power as is radiated.
  • There is a claim that Poynting’s theorem is derived from Maxwell’s equations, which connects the energy densities of capacitors, inductors, and EM waves.
  • Participants question why the energy densities of capacitors and inductors should be equivalent to those of EM waves.

Areas of Agreement / Disagreement

Participants express disagreement regarding the derivation of energy density from capacitors and inductors to EM waves. While some reference Poynting's theorem and Maxwell's equations as foundational, others contest the validity of these connections, indicating that the discussion remains unresolved.

Contextual Notes

There are limitations regarding the assumptions made about the derivation of energy density and the application of Poynting's theorem. The discussion does not resolve the mathematical steps involved or the definitions used in the context of energy density.

cg0303
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The energy density of an EM wave is given as (1/2) ϵ E^2 + (1/(2μ)) B^2.

This is derived from the energy density of the electric and magnetic fields of capacitors and inductors, respectively.

But why should the energy density of the fields of capacitors and inductors be the same as that of the fields of an EM wave?
 
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cg0303 said:
This is derived from the energy density of the electric and magnetic fields of capacitors and inductors, respectively.

No, it's not. Which book are you learning from? I mean, the book can say something like "let's assume it works also for EM waves" if it's not too advanced, but certainly there are textbooks that derive it the proper way.
 
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Check for the key word "Poynting's theorem"!
 
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Doesn't the Energy Conservation law apply here? The (ideal) passive components in a transmitter output network must be passing on the same Power as is being radiated.
 
sophiecentaur said:
Doesn't the Energy Conservation law apply here?
That's basically what the Poynting's theorem is.
 
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cg0303 said:
This is derived from the energy density of the electric and magnetic fields of capacitors and inductors, respectively.
No. It is derived from Poynting’s theorem, as I see several others have pointed out. Poynting’s theorem is derived directly from Maxwell’s equations.

cg0303 said:
But why should the energy density of the fields of capacitors and inductors be the same as that of the fields of an EM wave?
Because capacitors, inductors, and EM waves all obey Maxwell’s equations, therefore Poynting’s theorem describes the conservation of energy in all of them.
 
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