The Electric Charge Density in an Infinitely Long Cylinder

Understanding Electric Charge Density in an Infinitely Long Cylinder

The electric charge density in an infinitely long cylinder in the z-direction is symmetrical. The charge density is given by the expression ρ(r) = A/r2, where A is the total charge and r is the distance from the z-axis. This charge density is measured in coulombs per meter squared (C/m2).

The charge density in the cylinder can also be represented as ρ = λ / (2πr), where λ is the linear charge density and r is the radius of the cylinder. The distribution of charge density is symmetrical along the z-axis, which means it is the same at every point along the axis.

Furthermore, the charge density expression can be written in terms of the electric field, E, as ρ = ε₀E / (2πr), where ε₀ is the permittivity of free space. This equation relates the charge density to the electric field in the cylinder. The electric field in the cylinder is distributed symmetrically as well, depending only on the radius of the cylinder.

What is the expression for the electric charge density in an infinitely long cylinder in the z-direction? How is the charge density distributed in the cylinder?

The expression for the electric charge density in the cylinder is ρ(r) = A/r2, where A is the total charge and r is the distance from the z-axis. The charge density is distributed symmetrical along the z-axis, meaning it is the same at every point in the cylinder.