Electrostatics, Problem from D.J.Griffiths

[Khushidebo]

The Problem 3.20 of Chapter 3 (Special Techniques) of D. J. Griffiths 3rd Edition is:

"Find the potential outside a charged metal sphere (charge Q, radius R) placed in an otherwise uniform electric field E(0)(vector). explain clearly where are you setting zero of potential."

The Potential is that of such an uncharged sphere in the same electric field (potential due to the uniform filed added to the potential due to the induced charge) added to the potential due to the charged sphere (which behaves as if the charge is in its center).
THIS REPLY IS FINE FOR ME.
But for this they have set THE POTENTIAL AT AN EQUATORIAL PLANE FAR FROM THE CENTER TO BE ZERO as in the Example 3.8 from the book.

The Question now is WHY?
1. HOW CAN WE SET THE POTENTIAL AT AN EQUATORIAL PLANE ZERO.
THERE IS A DEFINITE POTENTIAL ON THE WHOLE SURFACE DUE TO PRESENCE OF THE CHARGE NOT LIKE ANY UNCHARGED SPHERE WHERE FOR OUR OWN CONVENIENCE WE CAN TAKE IT AS ZERO.

2. HOW CAN POTENTIAL FAR FROM THE SPHERE BE ZERO IF WE HAVE A UNIFORM ELECTRIC FIELD PRESENT EVERYWHERE OTHERWISE.

3. IF WE ARE DOING THIS BY TREATING TWO DIFFERENT CASES FOR CHARGED AND UNCHARGED POTENTIAL AND THEN ADDING THEM UP, THEN WHY THIS ASSUMPTION? IF SO, THEN HOW CAN THE POTENTIAL FOR THE SAME PROBLEM BE ONCE SET TO ZERO AT ONE PLACE THEN AT ANOTHER.

[rpenner]

Adding a constant to the electric potential does not change the electric field, and the electric field (equivalently, the difference between the electric potential at two places) is the only thing that physically matters in electrostatics.