- #1
quietrain
- 655
- 2
Homework Statement
why is the mean square radius of a sphere given as <r2> = 3/5 R2
The Attempt at a Solution
i saw this thread
https://www.physicsforums.com/showthread.php?t=293397
but i don't understand the helper (malawi_glenn)'s post
he put in a p(r), but what is that? density?
thanks!
malawi_glenn said:You are mixing concepts here, you have tried to evaluate the Form factor, F, with the potential r^2 ..
you want to evaluate the mean square radius, then use formula for distributions:
[tex]1 = A\int \rho (\vec{r})d\vec{r}[/tex]
this is from mathematical statistics. Now use that the distribution of charge is constant up radius R, and for radius larger than R it is zero. Angular integration gives you 4pi, so it is easy to find the normalization constant A.
Then you recall from statistics that the average value of some quantity Q is
[tex]<Q> = A\int Q\rho (\vec{r})d\vec{r}[/tex]
Now you have what you need.
What you did wrong was to mix this up with the Form factor F.