- #1
Mike400
- 59
- 6
The electric field due to a dipole distribution in volume ##V'## can be viewed as electric field due to a volume charge distribution in ##V'## plus electric field due to a surface charge distribution in boundary of ##V'##.
##\displaystyle\mathbf{E}=\int_{V'} \dfrac{\rho (\mathbf{r}-\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|^3} dV'
+ \oint_{S'} \dfrac{\sigma (\mathbf{r}-\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|^3} dS'=\mathbf{E}^{V}+\mathbf{E}^{S}##
##\mathbf{E}^{S}## is discontinuous at the surface ##S'##.
(1) Does this mean that ##\mathbf{E}^{S}## is undefined at the surface ##S'##? (Consequently ##\mathbf{E}## will be undefined at the surface ##S'##)
(2) If no, then what is ##\mathbf{E}^{S}## at the surface ##S'##?
##\displaystyle\mathbf{E}=\int_{V'} \dfrac{\rho (\mathbf{r}-\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|^3} dV'
+ \oint_{S'} \dfrac{\sigma (\mathbf{r}-\mathbf{r'})}{|\mathbf{r}-\mathbf{r'}|^3} dS'=\mathbf{E}^{V}+\mathbf{E}^{S}##
##\mathbf{E}^{S}## is discontinuous at the surface ##S'##.
(1) Does this mean that ##\mathbf{E}^{S}## is undefined at the surface ##S'##? (Consequently ##\mathbf{E}## will be undefined at the surface ##S'##)
(2) If no, then what is ##\mathbf{E}^{S}## at the surface ##S'##?