- #1
Mike400
- 59
- 6
Moved from a technical forum, so homework template missing
The dipole potential is given by:
##\displaystyle\psi=\int_{V'} \dfrac{\rho}{|\mathbf{r}-\mathbf{r'}|} dV'
+\oint_{S'} \dfrac{\sigma}{|\mathbf{r}-\mathbf{r'}|} dS'##
I need to prove that ##\psi## is differentiable at points except at boundary ##S'## (where it is discontinuous)
I know if partial derivatives of ##\psi## "exist and are continuous" everywhere except at boundary ##S'##, then ##\psi## is differentiable everywhere except at boundary ##S'##.
How shall I proceed in showing partial derivatives of ##\psi## exist?
Thanks for any help in advance.
##\displaystyle\psi=\int_{V'} \dfrac{\rho}{|\mathbf{r}-\mathbf{r'}|} dV'
+\oint_{S'} \dfrac{\sigma}{|\mathbf{r}-\mathbf{r'}|} dS'##
I need to prove that ##\psi## is differentiable at points except at boundary ##S'## (where it is discontinuous)
I know if partial derivatives of ##\psi## "exist and are continuous" everywhere except at boundary ##S'##, then ##\psi## is differentiable everywhere except at boundary ##S'##.
How shall I proceed in showing partial derivatives of ##\psi## exist?
Thanks for any help in advance.