Step 1: Understanding the Concept:
The electric field produced by an infinite plane sheet of charge is uniform and does not depend on the distance from the sheet. This is derived using Gauss's Law. When we place two such sheets parallel to each other with opposite charges, we can use the principle of superposition to find the total electric field in the various regions of space created by the plates (the region between them and the regions outside them).
Step 2: Key Formula or Approach:
1. Electric field ($E$) due to a single infinite sheet: $E = \frac{\sigma}{2\varepsilon_0}$.
2. Direction: The field points away from a positive sheet and towards a negative sheet.
3. Total field: $\vec{E}_{total} = \vec{E}_{pos} + \vec{E}_{neg}$.
Step 3: Detailed Explanation:
Let's define the two sheets: Sheet 1 has a charge density of $+\sigma$ and Sheet 2 has a charge density of $-\sigma$.
Consider a point located in the space between these two sheets.
The electric field produced by the positive sheet ($E_1$) points away from it, which means it points towards the negative sheet. Its magnitude is $\frac{\sigma}{2\varepsilon_0}$.
The electric field produced by the negative sheet ($E_2$) points towards it. This direction is the same as the direction of $E_1$. Its magnitude is also $\frac{\sigma}{2\varepsilon_0}$.
Since both individual fields point in the same direction at any point between the plates, we add their magnitudes to find the total field: $E = E_1 + E_2$.
$E = \frac{\sigma}{2\varepsilon_0} + \frac{\sigma}{2\varepsilon_0} = \frac{2\sigma}{2\varepsilon_0} = \frac{\sigma}{\varepsilon_0}$.
This resulting field is uniform and constant throughout the entire volume between the plates, regardless of the distance from either plate.
Step 4: Final Answer:
The electric field at any point between the sheets is $\frac{\sigma}{\varepsilon_0}$.