Derive an expression for the capacitance of a parallel plate capacitor in terms of the areas of the plates and the distance between them. Assume there is a vacuum in between the plates with the electric field between the plates `E=(sigma)/(epsilon_(0))` (where the symbols have their usual meaning).

Explanation

To derive the expression for the capacitance of a parallel plate capacitor, we will follow these steps:

### Step 1: Understand the Configuration
Consider a parallel plate capacitor with two plates, each having an area \( A \) and separated by a distance \( D \). One plate has a surface charge density \( +\sigma \) and the other has \( -\sigma \).

### Step 2: Electric Field Between the Plates
The electric field \( E \) between the plates can be expressed in terms of the surface charge density \( \sigma \) as:
\[
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