- #1

Yegor

- 147

- 1

Hallo!

Consider electrostatic Potential of point charge at point (0,0,0)

[tex]\phi = 1/r[/tex]

I'm trying to calculate [tex]\Delta\phi[/tex]

Actually it's not a difficult problem outside (0,0,0):

[tex]\nabla\phi = -\frac{\vec r}{r^3}[/tex]

[tex]\Delta\phi = 0[/tex]

But i also know, that i should become Dirac-Delta function (charge density for point particle). What is the problem in point (0,0,0)?

I understand that Potential goes there to infinity, but how can i work it out mathematically?

## Homework Statement

Consider electrostatic Potential of point charge at point (0,0,0)

[tex]\phi = 1/r[/tex]

I'm trying to calculate [tex]\Delta\phi[/tex]

## Homework Equations

## The Attempt at a Solution

Actually it's not a difficult problem outside (0,0,0):

[tex]\nabla\phi = -\frac{\vec r}{r^3}[/tex]

[tex]\Delta\phi = 0[/tex]

But i also know, that i should become Dirac-Delta function (charge density for point particle). What is the problem in point (0,0,0)?

I understand that Potential goes there to infinity, but how can i work it out mathematically?

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