- #1
davidbenari
- 466
- 18
Title doesn't let me be sufficiently clear so let me do it here:
The potential for a continuous charged object is ##V(\vec{r})=k\int\frac{dq}{|\vec{r}-\vec{r'}|}## and similarily for the electric field. This makes sense outside of the charged object but not inside!
Namely, I say it doesn't make sense inside because when you are integrating you will be considering all points having charge including the charge at point r. This would make the denominator in my integral blow up!
In the case of calculating energies for point charges it does blow up, and this problem has been called the "infinite self energy of the electron".
But why doesn't it blow up here? Is it some weird property of integrals that evade a singular point?
Thanks.
The potential for a continuous charged object is ##V(\vec{r})=k\int\frac{dq}{|\vec{r}-\vec{r'}|}## and similarily for the electric field. This makes sense outside of the charged object but not inside!
Namely, I say it doesn't make sense inside because when you are integrating you will be considering all points having charge including the charge at point r. This would make the denominator in my integral blow up!
In the case of calculating energies for point charges it does blow up, and this problem has been called the "infinite self energy of the electron".
But why doesn't it blow up here? Is it some weird property of integrals that evade a singular point?
Thanks.