Electric Fields of Cylinders: Understanding the Behavior

Understanding the behavior of the electric field inside different types of cylinders is essential in the study of electromagnetism. Let's delve deeper into the behavior of the electric field inside an infinite conducting cylinder and a uniformly charged cylinder.

Electric Field Inside an Infinite Conducting Cylinder:

Inside an infinite conducting cylinder, the electric field is zero. This phenomenon occurs due to the movement of free electrons within the conductor, which neutralizes the electric field inside. The absence of an electric field inside the conductor leads to unique properties in electromagnetism.

Electric Field Outside an Infinite Conducting Cylinder:

When considering the electric field outside an infinite conducting cylinder, it behaves as if there is an infinite line of charge. The electric field is directly proportional to the charge density and inversely proportional to the distance from the cylinder. Mathematically, this is expressed as E = λ/(2πε0r), where λ represents the linear charge density, ε0 is the permittivity of free space, and r is the radial distance from the cylinder.

Electric Field Inside a Uniformly Charged Cylinder:

For a uniformly charged cylinder, the behavior of the electric field inside is different. It increases linearly with the distance from the center of the cylinder. The equation representing the electric field inside a uniformly charged cylinder is given by E= ρr/(2ε0), where ρ represents the charge density.

Electric Field Outside a Uniformly Charged Cylinder:

On the other hand, the electric field outside a uniformly charged cylinder decreases with the inverse of the distance from the center of the cylinder. The formula for the electric field outside a uniformly charged cylinder is E= Q/(2πε0r), where Q is the total charge of the cylinder.

It is important to remember that these formulas are derived using Gauss's law, a fundamental principle in electromagnetism. Additionally, the direction of the electric field is radially outward for positive charges and radially inward for negative charges.