# 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

## 3 Answers

For Gauss' Law, which is derived from Poisson's equation, only the charge density matters irrespective where it resides. Therefore, the electric fields are equal for the conducting or non-conducting infinite sheets with equal total areal charge densities 𝜎. It should be noted that in the case of the conducting infinite sheet, equal sheet charge densities exist at both conductor/vacuum interfaces whose sum represent the total areal charge density 𝜎 of the conductor sheet.

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 $|\mathbf{E}| = \frac{\sigma}{2\epsilon_0}$.

ACTUALLY THE ELECTRIC FIELD INTENSITY REMAINS SAME I) IN CASE OF NON CONDUCTING SHEET THE CHARGE LIES ON ONE SIDE OF THE SHEET SO CHARGE DENSITY IS CHARGE DIVIDED BY SURFACE AREA( ONE SIDE OF THE SHEET) ELECTRIC FIELD INTENSITY = CHARGE DENSITY/2*EPSILON II) IN CASE OF CONDUCTING SHEET THE CHARGE LIES ON BOTH SIDE OF THE SHEET SO CHARGE DENSITY IS CHARGE DIVIDED BY SURFACE AREA OF BOTH SIDE OF THE SHEET. SO CHARGE DENSITY GETS HALVED. NOW ELECTRIC FIELD INTENSITY = CHARGE DENSITY/EPSILON , AS CHARGE DENSITY GETS HALVED SO AGAIN ELECTRIC FIELD INTENSITY REMAINS SAME.