Try

E_rho = magnitude of E in the r direction as (x^2 + y^2) where x and y are the magnitudes of E in the x and y directions of Cartesian cords.

E_ phi = magnitude of E in the phi direction as arctan y/x where x and y are the magnitudes of E in the x and y directions of Cartesian cords.

I think you may be confusing a bit of spherical coords in here.

E_rho = magnitude of E in the r direction as (x^2 + y^2) where x and y are the magnitudes of E in the x and y directions of Cartesian cords.

E_ phi = magnitude of E in the phi direction as arctan y/x where x and y are the magnitudes of E in the x and y directions of Cartesian cords.

I think you may be confusing a bit of spherical coords in here.