The definition of voltage I'm familiar with is the amount of electric potential energy per unit charge at a location. My prof defined the voltage of a battery to be the amount of potential energy difference an unit charge would have at the positive terminal vs. the negative terminal.
But from what I remember from high school, the "terminals" aren't points, their rods of metal:
Since the voltage is defined at a point, not cylinders or rods what does the voltage of a battery mean? Also, how does the definition connect to the "pushing" power of a battery?
I took a look at Electrode Potential but it was a bit over my head.
I'm looking for an intuitive explanation, not one using rigorous chemistry concepts. Thanks!