A long cylinder contains charge distributed uniformly having volume charge density ρ.

What is the electric field at a point P inside the cylinder at a distance x from its axis?

ρx/2ε₀

$\text{Consider a cylindrical Gaussian Surface of radius x and length l }$

$\text{Electric Flux through this gaussian surface is }E.2\pi xl = \frac{q_{in}}{\epsilon_0} = \frac{\rho \pi x^2 l}{\epsilon_0}$

$\Rightarrow  E = \frac{\rho x}{2\epsilon_0 }$