UY1: Electric Field Of Two Oppositely Charged Infinite Sheets


Two infinite plane sheets are placed parallel to each other, separated by a distance d. The lower sheet has a uniform positive surface charge density $\sigma$, and the upper sheet has a uniform negative surface charge density $- \sigma$ with the same magnitude. Find the electric field between the two sheets, above the upper sheet, and below the lower sheet.

From Electric field of a uniformly charged disk, electric field of an infinite sheet is:

$$E_{1} = E_{2} = \frac{\sigma}{2 \epsilon_{0}}$$

 

infinite sheets

 

From the diagram above, we can see that the field between the two sheets are added together to give $E = \frac{\sigma}{\epsilon_{0}}$. The electric field at the sides cancels.

If you are not satisfied with this explanation, you can use Gauss’ law to come to the same conclusion.

 

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