In Fig. 25-40, two parallel-plate capacitors (with air...

In Fig. $25-40,$ two parallel-plate capacitors (with air between the plates) are connected to a battery. Capacitor 1 has a plate area of 1.5 $\mathrm{cm}^{2}$ and an electric field (between its plates) of magnitude 2000 $\mathrm{V} / \mathrm{m} .$ Capacitor 2 has a plate area of 0.70 $\mathrm{cm}^{2}$ and an electric field of magnitude 1500 $\mathrm{V} / \mathrm{m} .$ What is the total charge on the two capacitors?

In Fig. $25-40,$ two parallel-plate capacitors (with air between the plates)
are connected to a battery. Capacitor 1
has a plate area of 1.5 $\mathrm{cm}^{2}$ and an electric field (between its plates) of magnitude
2000 $\mathrm{V} / \mathrm{m} .$ Capacitor 2 has a plate area of 0.70 $\mathrm{cm}^{2}$ and an electric field of magnitude 1500 $\mathrm{V} / \mathrm{m} .$ What is the
total charge on the two capacitors?

Key Concepts

Parallel-Plate Capacitor

A parallel-plate capacitor consists of two conductive plates separated by a small distance, creating a uniform electric field between them when a voltage is applied. This geometry provides a basis for calculating capacitance, which depends on the plate area, the separation distance, and the permittivity of the dielectric between the plates.

Capacitance and Charge Storage

Capacitance is a measure of a capacitor’s ability to store electric charge per unit voltage. The relation Q = CV (where Q is charge, C is capacitance, and V is voltage) is fundamental in determining how much charge is stored for a given potential difference, highlighting the role of capacitor geometry and the dielectric properties.

Electric Field and Surface Charge Density

In a parallel-plate capacitor, the electric field is uniform between the plates and is related to the surface charge density by E = Q/(?? A), where Q is the charge on a plate, A is the area of the plate, and ?? is the permittivity of free space. This relation helps to directly connect the measurable field to the stored charge.

Permittivity of Free Space (??)

Permittivity of free space, denoted by ??, is a fundamental physical constant that plays a key role in electrostatics. It appears in various electromagnetic equations including the ones describing the capacitance of a parallel-plate capacitor and the relationship between the electric field and surface charge density.

Unit Conversion in Electrical Calculations

Correct unit conversion is essential in physics problems to ensure consistency in calculations. For capacitor problems, it is often necessary to convert units such as area (for example, from square centimeters to square meters) to maintain the accuracy of calculations involving physical constants and derived quantities.

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