Why does the linear antenna radiate at k^2?

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Discussion Overview

The discussion centers on the radiation characteristics of a linear antenna, specifically a dipole, as described in Jackson's classical electrodynamics. Participants explore the relationship between the dipole moment and the power radiated, referencing specific equations from the text.

Discussion Character

  • Technical explanation

Main Points Raised

  • One participant notes that Jackson's book states the total power radiated by a dipole is proportional to k^4, while questioning why it is indicated to radiate at k^2 in a specific equation.
  • Another participant suggests that the dipole moment includes a term with ω in the denominator, which affects the proportionality of the power radiated.
  • A subsequent participant questions whether the real power for a dipole should indeed be proportional to k^2 instead of k^4.
  • One participant confirms the assertion that the power should be proportional to k^2.

Areas of Agreement / Disagreement

The discussion reflects some agreement on the proportionality of power radiated by a dipole being k^2, but it is based on interpretations of the equations presented in the text, leaving some aspects unresolved.

Contextual Notes

Participants reference specific equations from Jackson's book, which may involve assumptions about the definitions and conditions under which these equations apply. The discussion does not resolve the implications of these equations fully.

qnach
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I am reading Jackson's book on classical electrodynamics.
It said in page 412 to 415 (3rd edition) that the total power radiated by a
dipole is proportional to k^4 (equation 9.24)
quadrupole is proportional to k^6 (equation 9.49)
But why does the linear antenna at page 412, which is a dipole, radiate at k^2 (equation 9.29)?
 
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The dipole moment, p, has ω in the denominator (equation 9.27). Thus the c2|p|2 terms in 9.24 replace two of the k's.
 
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so the (real) power for a dipole should be proportional to k^2 instead of k^4 ?
 
Yes
 

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