Cylindrical Capacitor: Understanding Electric Fields Between Two Concentric Cylinders

The electric field in between two concentric cylinders of a cylindrical capacitor with charges -q and q is directed from the outer cylinder towards the inner cylinder, and its magnitude is given by E = -q / (2πrlε).

Explanation:

When dealing with a cylindrical capacitor consisting of two concentric cylinders, with the inner cylinder carrying a charge of -q and the outer cylinder carrying a charge of q, the electric field that exists between these cylinders can be determined using Gauss's law.

Gauss's law allows us to find the relationship between the electric field and the total charge enclosed within a Gaussian surface. In this case, we consider a cylindrical Gaussian surface with a radius r and height l.

Since the inner cylinder carries a total charge of -q, the total charge enclosed within our chosen Gaussian surface is -q. Applying Gauss's law, we arrive at the equation: E = -q / (2πrlε), where ε represents the permittivity.

The negative sign in the equation indicates that the electric field points from the outer cylinder towards the inner cylinder. This directionality aligns with the relative charges present on the cylinders: negative on the inner cylinder and positive on the outer cylinder.

The magnitude of the electric field is dependent on the amount of charge and the dimensions of the capacitor, specifically the radii and length of the cylinders involved. The formula E = -q / (2πrlε) provides a quantitative understanding of how these factors affect the strength of the electric field.