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Point charge potential

  • Thread starter Yegor
  • Start date
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1
Hallo!

1. 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]

2. Homework Equations

3. 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?
 
Last edited:

Answers and Replies

Meir Achuz
Science Advisor
Homework Helper
Gold Member
2,169
63
Using the integral definition of div, it can be shown that
div(r(vec)/r^3)=4pi delta(r).
This can also be shown by appying the div theorem and taking the limit as r-->0.
What book are you using? Graduate texts do this.
 

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