Gauss's Law applied to an E-Field and Cylindrical Surface

Closed surface integration of an electric field using a cylindrical Gaussian surface.

My team helped me understand how Ansys was able to get matching results. I learned that we need to create something called a  Face List to use as the Gaussian surface and we should not use the surface geometry named after the vacuum objects we have in the model.

To create a Face List just select the object you want to use for the Gaussian surface, then right click and select Extend Selection > All Object Faces.

Then select Modeler and choose List > Create > Face List

In the Field's Calculator copy the E vector to the stack and select Normal. In the Field's Calculator this Gaussian surface will be available to use in your closed surface integration of the E Field. Copy the Gaussian surface to the stack and select integrate.

Then the result obtained from integrating the charge density on the conductor should match with the results obtained by integrating the E Field over the closed surface. You would need to create a Face List for each object that is intended to use for the Gaussian surface. Please let me know if you have any questions.