Electric Field Between Two Co-Aligned Conducting Cylinders

What determines the magnitude of the electric field between the outer cylinder and the inner cylinder?

Is the magnitude of the electric field dependent on the radius of the cylinders or the surface charge densities?

Answer:

The magnitude of the electric field between the outer cylinder and the inner cylinder is determined by both the radius of the cylinders and the surface charge densities.

When calculating the electric field between the outer and inner cylinders, we consider the charges present on the surfaces of the cylinders. The surface charge densities ps1 and ps2 along with the radii of the cylinders a and b play a crucial role in determining the electric field strength.

By using Gauss's law, we can analyze the electric flux through a cylindrical Gaussian surface positioned between the cylinders. The charges enclosed within this surface contribute to the electric field between the cylinders. The calculations involve the charges on the inner and outer surfaces of the cylinders, which are related to the surface charge densities and the lengths of the cylinders.

The formula for the magnitude of the electric field between the outer and inner cylinders takes into account the contributions from both surface charge densities on the cylinders. Hence, the radius of the cylinders and the surface charge densities collectively determine the strength of the electric field between the co-aligned conducting cylinders.