# Force between charged plates

1. Sep 12, 2009

### bodensee9

1. The problem statement, all variables and given/known data
Two charged plates, plate 1 and plate 2, are separated by a distance s. Plate 1 has charge density $$\sigma_{1}$$ and plate 2 has charge density $$\sigma_{2}.$$ Assume that the electric field to the left of plate 1 is $$E_{1},$$ in between the 2 plates is $$E_{2},$$ and to the right of plate 2 is $$E_{3}.$$ Find the force per unit area of this configuration (I guess assume that somehow these two plates were connected).

3. The attempt at a solution

Assume Gaussian units:
So would I do $$dF = \int Edq$$ and so assume that the plates have a width called say r, then for plate 1,
$$F = \int E\sigma_{1}dr$$ from 0 to r
and since by Gauss' Law, $$dE = 4\pi\sigma_{1}$$, so I have
$$F = \int \frac{EdE}{4\pi}$$ evaluated from $$E_{1}to E_{2}.$$
Then I have $$F = \frac{E_{2}^{2}-E_{1}^{2}}{8\pi}.$$ BUt since I know that
$$E_{2}-E_{1} = 4\pi\sigma_{1}$$ so this is $$\frac{(E_{1} + E_{2})\sigma_{1}}{2}?$$ And that would be the force. I would do the same thing for plate 2? Thanks.

Last edited: Sep 12, 2009
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