Electric Field Outside a Charged Cylinder
The electric field outside a charged cylinder can be calculated using Gauss's law. The electric field at a distance r from the axis of the cylinder is given by E = kλ/r, where λ is the linear charge density of the cylinder.

Gauss's Law
Gauss's law states that the electric flux through a closed surface is equal to the charge enclosed by the surface divided by the permittivity of free space. Mathematically, this can be expressed as Φ = q/ε₀, where Φ is the electric flux, q is the charge enclosed, and ε₀ is the permittivity of free space.

Applying Gauss's Law to a Charged Cylinder
To find the electric field outside a charged cylinder, we consider a cylindrical Gaussian surface with radius r > R (radius of the cylinder). The electric flux through this surface is given by Φ = E(2πrL), where L is the length of the cylinder.

Calculating Electric Field
Using Gauss's law, we have Φ = q/ε₀ = λL/ε₀. Equating this with E(2πrL), we get E = λ/(2πε₀r), which simplifies to E = kλ/r, where k = 1/(2πε₀).
Therefore, the electric field outside a charged cylinder is given by E = kλ/r, where k is a constant and λ is the linear charge density of the cylinder.