Continuity of the first Maxwell equation.

[Bert]

Suppose that we will proof the continuity of the first maxwell equation:

So we have $$div(\vec{E})=\frac{1}{\epsilon _0} \rho$$ than $$\iiint \ div(\vec{E}) = \oint_v \vec{E} d\vec{s}=\iiint \frac{1}{\epsilon _0 } \rho$$
than follewed $$E_{y1} l -E_{y2}l=Q$$

Therefore E must continue is this a good proof? Thanks.

 

[ZapperZ]

You have not defined what "y" direction is. So your y components are ambiguous.

Only the parallel component of the E-field (parallel to the surface) is continuous.

Zz.

 

[Bert]

Thanks if I define my y component as the parallel one. Is than the proof oké?