Parallel Plate Capacitor and distance

[Trista]

I'm going through my book and one of the Example exercises has the following problem:
Two plates, each of area 3X10^-4 m^2 are used to construc a parallel-plate capacitor with capacitance 1 pF. (a) Find the necessary separation distance.

Seems pretty obvious right? C = Eo(A/d)
So, I figure I'm finding d = C/(Eo)(A)
but it doesn't come out right, so I must be missing something either in my math (not surprising) or the area. Do I need to do a calculation with the area? Like 2 X A? That doesn't work either, and it doesn't seem right to do it that way. Help, please??

 

[Hootenanny]

Its just your manipulation which is letting you down. It should be;

$$C = \frac{E_{0}A}{d}$$
$$C \cdot d = E_{0}\cdot {A}$$
$$d = \frac{E_{0}A}{C}$$

-Hoot

 

[Trista]

Its just your manipulation which is letting you down.

You are awesome! Thank you!

 

[Ouabache]

If you are assume the dielectric is air (k ~ 1) and $\epsilon_o = 8.854 x 10^{-12}$ F/m, you may get d = 2.656 mm. A more general formula for this type question may be found here.
In agreement with Hoot, i noticed the same fault in rearranging your equation. It is a good idea to do a couple of things to double check maths. One is to do the algebra step by step, the other is to do a quick dimensional analysis of the final equation. In your case, you have A left in the denominator. The only way that would work and have answer come out in meters is to have $m^3$ in the numerator, which you don't have.

 

[Trista]

Wow. Thank you, that is most helpful. The link is terrific. Again, thank you!