- #1
ozone
- 122
- 0
Sorry guys I have a lot of trouble with proofs and could use your help with this one.
This is right out of Griffiths (problem 2.29) I have a solution manual, but I'd like to try to get a nudge in the right direction before I turn to it.
Poisson's eq:
[itex]\nabla ^2 V = - \frac{ \rho }{\epsilon }[/itex]
Using an identity out of Griffiths we have [itex]\nabla ^2\left(\frac{1}{r}\right) = -4\pi \delta ^3(r)[/itex]
finally we know that [itex] V(r) = \frac{1}{4\pi \epsilon }\int \frac{p(r')}{r} \, dr'[/itex]
distributing the gradient into our function will yield
[itex]V(r) = -\frac{1}{\epsilon }\int p(r')\delta ^3(r)dr'[/itex]
But I do not know what to do with the dirac delta in the final function we have arrived at.
This is right out of Griffiths (problem 2.29) I have a solution manual, but I'd like to try to get a nudge in the right direction before I turn to it.
Poisson's eq:
[itex]\nabla ^2 V = - \frac{ \rho }{\epsilon }[/itex]
Using an identity out of Griffiths we have [itex]\nabla ^2\left(\frac{1}{r}\right) = -4\pi \delta ^3(r)[/itex]
finally we know that [itex] V(r) = \frac{1}{4\pi \epsilon }\int \frac{p(r')}{r} \, dr'[/itex]
distributing the gradient into our function will yield
[itex]V(r) = -\frac{1}{\epsilon }\int p(r')\delta ^3(r)dr'[/itex]
But I do not know what to do with the dirac delta in the final function we have arrived at.