Question

A simple capacitor is a device formed by two insulated conductors adjacent to each other. If equal and opposite charges are placed on the conductors, there will be a certain difference of potential between them. The ratio of the magnitude of the charge on one conductor to the magnitude of the potential difference is called the capacitance (in SI units it is measured in farads). Using Gauss's law, calculate the capacitance of two large, flat, conducting sheets of area A, separated by a small distance d;

Answer 1

Capacitance of a parallel-plate capacitor can be calculated using Gauss's law, resulting in a formula where capacitance is the permittivity of free space times the area of the plates divided by their separation distance, C = ε0A/d.

Step-by-step explanation:

The question pertains to calculating the capacitance of a parallel-plate capacitor using Gauss's law. Given that we have two large, flat, conducting sheets with an area A and separated by a small distance d, the capacitance C can be determined by the arrangement's geometry and the insulating material between the conductors. From the description provided, it's assumed that we're dealing with a vacuum capacitor (no dielectric material), and consequently, the capacitance would be directly proportional to the area of the plates and inversely proportional to the separation distance between them. Using the equation from Gauss's law that the electric field E is the charge density σ over the permittivity of free space ε0, and the definition of capacitance as the charge Q per voltage V, we can deduce that C = ε0A/d.