Electric field due to a Long Uniformly Charged Solid Cylinder

Field due to a Long Uniformly Charged Solid Cylinder

Let  be the volumetric charge density and R be the radius of the cylinder



Here, the field is radically away from x-axis having a cylindrical symmetry.

Case I : r > R. Consider a Gaussian cylinder of length I and radius r about x-axis. Electric field lines come out radically. Let E be the magnitude of electric field, then 

. Now by Gauss law,




Case II : r < R.





By Gauss law