Electric Field Intensity Outside a Uniformly Charged Cylinder

What is the formula for the electric field strength outside a long charged cylinder?

The electric field intensity outside a long charged cylinder of radius R with linear charge density λ is given by Gauss's law as E = λ / (2πε0r) where r ≥ R.

How is the electric field intensity outside a long charged cylinder calculated?

The electric field intensity outside a long charged cylinder is calculated using Gauss's law. Gauss's law states that the integral of the electric field times the area over a closed surface is equal to the total charge contained within that closed surface divided by the permittivity of free space (ε0).

First, we define a Gaussian surface as a cylinder with a radius r (r ≥ R) and length L. The Gaussian surface encloses some of the charge on the uniformly charged cylinder.

Then, since the electric field strength E is radially outward and is the same at all points on the Gaussian surface, the total outward electric flux Φ through the surface is simply E multiplied by the total area of the cylinder, which is E × 2πrL = Qenc/ε0, where Qenc is the enclosed charge = λL. Therefore, after canceling L and rearranging, we get E = λ/2πε0r outside the charged cylinder (r ≥ R).