Subject: Motion within an electrical potential

Hi, I have amended my phrasing slightly in this resubmitted question.

Excluding all other gravitational influences, inside a hollow sphere there is 
no gravitational field but there is a gravitational potential that has the 
same value at every point within the sphere. Analogously, I 
presume that within a hollow conducting sphere while there may be no 
electrical field, there is an electrical potential that, likewise, has the 
same value at every point within the sphere. My question below concerns what 
happens when a non-charged object moves within this electrical potential. 

My question is this: If we allow a non-charged object to move with a certain 
fixed velocity (i.e. not to accelerate, but rather to "drift") within this 
electrical potential, what happens? What effect results, if any? Does this 
motion produce a current, an electric field, or some other effect? In which 
direction is any force directed that might be produced by this moving object? 
Mathematically, how is this motion described? Show me your calculations or 
equations, please. (For instance, do we take the derivative of the electric 
potential to calculate the magnitude of this supposed force or effect 
resulting from the motion?)

What if the moving object is charged? What if it accelerates within the sphere 
(by changing direction or speeding up, etc.)? Many thanks for your help! (I 
have not been able to answer the questions above in checking assorted 
textbooks.)

Andrew

Re: Motion within an electrical potential