What Are the Correct Units for the Larmor Formula?

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Discussion Overview

The discussion revolves around the correct units for the Larmor formula, specifically addressing the dimensional analysis of the formula and whether the derived units correspond to power in watts. The scope includes technical reasoning and unit analysis within the context of physics.

Discussion Character

  • Technical explanation, Debate/contested

Main Points Raised

  • One participant presents the Larmor formula and performs a dimensional analysis, concluding that the units appear to be [kg m^2 s^-1], questioning if they should instead be [kg m^2 s^-3] for watts.
  • The same participant provides the units for each component of the formula, noting that they used SI units.
  • Another participant challenges the correctness of the formula without providing further details, later retracting their statement.
  • A third participant corrects the first participant's analysis by stating that the units of acceleration are m/s², leading to the conclusion that the units of a² should be m²/s⁴ instead of m²/s².
  • The first participant acknowledges the correction and expresses self-deprecation regarding their error.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the Larmor formula itself, and there is disagreement regarding the initial dimensional analysis, which is later corrected by another participant.

Contextual Notes

The discussion highlights potential misunderstandings in dimensional analysis and unit conversions, but does not resolve the correctness of the Larmor formula itself.

bdforbes
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The Larmor formula is:

P=\frac{\mu_0 q^2 a^2}{6\pi c}

When I checked the units of this, I got [kg m^2 s^-1]. If it is in watts, shouldn't it be [kg m^2 s^-3]? I was pretty thorough in putting everything in SI units.

\mu_0 is N/A^2 or kg m s^-2 A^-2.
q^2 is C^2 or A^2 s^2
a^2 is m^2 s^-2
c is m s^-1

Have I made a stupid error, or is this just the wrong way of doing the dimensional analysis?

This is not homework.
 
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I don't think the formula is right.

edit: Never mind. :P
 
Last edited:
The units of acceleration are m/s^2 not m/s, so the units of a^2 are [/itex]m^2/s^4[/itex] not [/itex]m^2/s^2[/itex].
 
Stupid error it is then, thanks :P. You'd think after 4 years of uni I might be able to get that one right...
 

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