Final answer:
When the electric potential at the surface of a uniformly charged non-conducting sphere is redefined from V to zero, the potential at the center of the sphere becomes -3V/2, based on electrostatic principles.
Step-by-step explanation:
If the electric potential at the surface of a uniformly charged non-conducting solid sphere made of material with dielectric constant one is taken to be zero instead of V at infinity, then the potential at the center of the sphere becomes important to consider.
Using the principle that the potential inside a conductor is constant and equal to the potential on its surface, and that the electric field inside a conductor in electrostatic equilibrium is zero, we can determine the potential at the center when we redefine the potential at the surface to be zero.
From the given information, and the principles of electrostatics, we can deduce that if the potential at the surface is now zero (instead of V), the potential at the center of the sphere would be -3V/2.
This is because the potential inside the sphere would have been V before redefining the surface potential to zero, and the change from the surface to the center inside the sphere would have originally been +V/2 (making it V at the center since we were considering V at the surface).
When we change the surface potential to zero, we are effectively reducing the potential at the center by V (which was the original surface potential), hence it becomes -3V/2.