# Conducting and non-conducting infinite sheets of charge have same $E$? ($E$= electric field intensity)?

From my textbook the description is given below to the image.

• What happens when I place two non-conducting sheets with the same surface charge density next to each other, say, separated by a distance $d$? – Sean E. Lake Aug 28 '16 at 7:29
• Related: physics.stackexchange.com/q/65191/2451 and links therein. – Qmechanic Aug 28 '16 at 7:59

The answer is that the change in the component of the electric field that is perpendicular to the sheet of charge is: $$\hat{n}\cdot \Delta \mathbf{E} = \frac{\sigma}{\epsilon_0}.$$ Specifically, $\hat{n}$ is the unit vector perpendicular to the sheet of surface charge. This is true no matter where the sheet is as long as it is smooth enough to be flat if you zoom in enough. In the case of the conductor you have a condition that the electric field inside of it is $\mathbf{0}$, so the electric field outside will be $\sigma / \epsilon_0$. With an isolated infinite sheet that is the only source of electric fields in the universe you have a symmetry that the field on either side has to have the same magnitude, even if the directions are opposite, giving $|\mathbf{E}| = \frac{\sigma}{2\epsilon_0}$.