# I Why electric field between two plates $\frac {σ} {ε_0}$ ?

1. Feb 20, 2017

### Arman777

Why electric field between two plates $\frac {σ} {ε_0}$ ? Where is that came from ?

2. Feb 20, 2017

### cnh1995

Gauss' law.

3. Feb 20, 2017

### Arman777

ohh we didnt learn it.But we will..I guess I should wait then

4. Feb 20, 2017

### cnh1995

5. Feb 20, 2017

### Arman777

I didnt understans...I will ask in class

6. Feb 20, 2017

### Staff: Mentor

There is another way of getting the result, by integrating vectorially the field created by each differential element of area of each plate.

7. Feb 20, 2017

### Staff: Mentor

8. Feb 20, 2017

### Arman777

Yeah we will learn gauss law in couple weeks

9. Feb 21, 2017

### taco01

When using two plates, they are normally placed very close to each other. The distance of separation is extremely small compared to the size of the plates. This is essentially the concept of an "infinite sheet." An infinite sheet is an infinitely large, charged sheet. Technically, the electric field due to an infinite sheet is: http://tinypic.com/r/hss6jn/9 http://imageshack.com/a/img924/8000/MPvupe.png (application of Coulomb's law). R is the measure of a dimension of the sheet, and its proportional to the area of the sheet. x is the distance from the sheet to a point. Since the sheet is infinitely large, R is infinitely large and is therefore much greater than x, so 1/ (√(r^2 / x^2) +1) becomes extremely small, to the point where it no longer has an impact on the magnitude of the electric field. Since x does not have an effect on the magnitude of the electric field, the electric field has the same magnitude at every point. The electric field then becomes: E = σ/(2ε_o). The electric field between two plates is twice the magnitude, and that's where your equation comes from.