Consider the attraction and repulsion of different types of charge.
a) Explain why you expect to find that the amount of charge a battery can pump onto a parallel plate capacitor will double if the area of each plate doubles.
To understand why the amount of charge a battery can pump onto a parallel plate capacitor will double if the area of each plate doubles, we need to consider the concept of electric field strength between the plates.
A parallel plate capacitor consists of two conductive plates separated by a small distance. When a battery is connected to the capacitor, it creates a potential difference (voltage) between the plates, which creates an electric field between them.
According to Gauss's Law, the electric field between the plates of a parallel plate capacitor is directly proportional to the charge density (amount of charge per unit area) on the plates. Mathematically, this relationship can be expressed as:
E = σ / ε₀
Where:
E is the electric field strength,
σ is the charge density on the plates, and
ε₀ is the permittivity of free space.
Now, let's consider the scenario where the area of each plate doubles. If we assume that the total charge pumped onto the plates remains the same, the charge density (σ) on each plate will decrease since the same amount of charge is spread across a larger area. As a result, the electric field strength (E) between the plates will also decrease.
However, the voltage provided by the battery remains the same, as it is determined by the potential difference between the plates. This means that the decrease in electric field strength is compensated by the increase in distance between the plates, resulting in a uniform electric field across the larger area.
Now, if we want to maintain the same electric field strength as before (prior to doubling the plate area), we need to double the charge density on each plate. Since the charge density is directly proportional to the amount of charge (Q) on each plate, doubling the plate area will require doubling the amount of charge.
Therefore, we expect that the amount of charge a battery can pump onto a parallel plate capacitor will double if the area of each plate doubles, in order to maintain the same electric field strength between the plates.