- #1

Shawnyboy

- 5

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**Hello Physics Peeps,**

It just came up in the notes for my electrodynamics class that an electrons charge squared can be expressed as the radius times the mass times the speed of light squared.

[itex] e^2 = m_er_ec^2[/itex]

It just came up in the notes for my electrodynamics class that an electrons charge squared can be expressed as the radius times the mass times the speed of light squared.

[itex] e^2 = m_er_ec^2[/itex]

**I don't understand the motivation for doing this. I've tried to search for other people doing this online to no avail. Is this just some kind of weird approximation or is it actually valid? If so why?**

As far as I can see the units don't even match up although I may be missing something we have energy times distance on the right, charge on the left.

For a little more context this came up in a problem about synchroton radiation where we were using the formula for power emitted by an electron in a synchrotron which is:

[itex] P = \frac{2e^2}{3c}\omega^2\beta^2\gamma^4 [/itex]

And by using the relation in question we simplified the question by saying:

[itex] \frac{2e^2}{3c} = \frac{2(.5MeV)(2.8*10^{-13}cm)}{3c} \approx 3 * 10^{-24 }MeV s [/itex]

Thanks for any help you can give me

As far as I can see the units don't even match up although I may be missing something we have energy times distance on the right, charge on the left.

For a little more context this came up in a problem about synchroton radiation where we were using the formula for power emitted by an electron in a synchrotron which is:

[itex] P = \frac{2e^2}{3c}\omega^2\beta^2\gamma^4 [/itex]

And by using the relation in question we simplified the question by saying:

[itex] \frac{2e^2}{3c} = \frac{2(.5MeV)(2.8*10^{-13}cm)}{3c} \approx 3 * 10^{-24 }MeV s [/itex]

Thanks for any help you can give me