Welcome to our site! EDAboard.com is an international Electronic Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.
Changing er affects your patch size, which will affect the far field, because if the increased dimension of your aperture.
I don't think your thought process for the radiated field is correct. Once it is radiated, it is propagating in air, and so the only thing that will really affect the far field boundary is how big the antenna is (and of course the wavelength).