# Electron charge^2 as a product of radius, mass, and c^2?

• Shawnyboy
In summary, the equation e^2 = m_er_ec^2 can be used to approximate the radius of an electron. This approximation is valid if you use cgs units, but it may not be accurate if you use other units.
Shawnyboy
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.

$e^2 = m_er_ec^2$

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:

$P = \frac{2e^2}{3c}\omega^2\beta^2\gamma^4$

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

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

Thanks for any help you can give me

What unit system are you using? cgs perhaps? and mind the equivalence of e-v and Joules.

Shawnyboy
Ah-hah! cgs! That at least explains the units, because according to wikipedia a Statcoulomb = erg^1/2 * cm^1/2. However it is still not entirely clear the motivation. I mean you can't just do something because the units work.

It's maybe a definition of some electron "radius".
e^2/r is an electrostatic energy. mc^2 is the rest energy.

I think that nasu is right. The electron is a quantum "point particle" meaning that it has no internal structure. The electron doesn't have a radius, per se, not in quantum mechanics and not classically either.

Easy Googling, folks! Compton radius is the name for what you get when equating rest mass with electrostatic energy.

But beware, you end up with superstition and fantasy in no time...
For all we know, electrons are pointlike. And yet they aren't obeying all the expected accompanying behaviour rules.
Can't find a reasonable quotation for the upper limit; thought it was around 10-30 m. Anyone know where to look ?

Shawnyboy
BvU said:
Easy Googling, folks! Compton radius is the name for what you get when equating rest mass with electrostatic energy.

But beware, you end up with superstition and fantasy in no time...
For all we know, electrons are pointlike. And yet they aren't obeying all the expected accompanying behaviour rules.
Can't find a reasonable quotation for the upper limit; thought it was around 10-30 m. Anyone know where to look ?
Thank You! That's exactly what it is. That explains it perfectly, although a strange concept this "Compton Radius". I wonder how useful it actually could be. It seems very incorrect to think of an electron in this way.

## 1. What is the equation for calculating electron charge squared?

The equation for calculating electron charge squared is Q2 = (4πε0)-1(mec2)2r2, where Q is the electron charge, ε0 is the permittivity of free space, me is the mass of the electron, c is the speed of light, and r is the radius of the electron's orbit.

## 2. How does the radius of an electron's orbit affect its charge squared?

The radius of an electron's orbit is directly proportional to its charge squared. This means that as the radius increases, the charge squared also increases. This relationship is described by the equation Q2 ∝ r2.

## 3. What is the significance of the speed of light in the equation for electron charge squared?

The speed of light, denoted by c, is a constant in the equation for electron charge squared. This constant represents the maximum speed at which any object, including an electron, can travel. It is also a fundamental constant in the theory of relativity and plays a crucial role in understanding the behavior of subatomic particles.

## 4. How is the electron charge squared related to the electron's mass?

The electron charge squared is indirectly proportional to the electron's mass. This means that as the mass of the electron increases, the charge squared decreases. This relationship is described by the equation Q2 ∝ 1/m2.

## 5. Can the equation for electron charge squared be used for other subatomic particles?

Yes, the equation for electron charge squared can be used for other subatomic particles, but the values for the constants and variables will differ according to the specific particle. For example, the mass and charge of a proton or a neutron can be substituted into the equation to calculate their respective charge squared values.

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