I'm taking an electromagnetic theory course, but I have trouble understanding the field and potential inside and outside of a conductive sphere when it is connected and not connected to ground. And why is the voltage inside the ball connected to the ground zero?
The conducting sphere is a Faraday cage: The field inside it is zero. What does the grounding do for that? Nothing!
Remember that the electric field is the gradient of the potential and does not change when you add a constant to the potential. What the grounding does is fix that constant.