Voltage is defined as:
Given the circuit: 
Why would potential not drop, from the point differentially away from the positive terminal on the battery, to the point I have labeled. I understand that charges lose energy in resistors due to inter lattice collisions, where the acceleration generated due to thermal motion and voltage bias is translated from kinetic energy to heat energy. Before the resistor the resistance is neglible so the drift velocity will be high, and collsions will be minimal. Even so as the charges move from the positve terminal the Electric field will be strong and we will be losing the potential energy as we travel in the direction of the field. With this so why dosent potential drop as we move in the direction of the field? Is the energy associated with the charge essentially translated from potential to kinetic energy, where very little of this kinetic energy is translated to heat energy, and we assume the total potential is associated with the total energy the charge has at this point (KE + PE)?
I am really looking for an answer to my question. It would be much appreciated if we address the core question I asking instead of side discussions! After the initial answer, I encourage side discussions if wanted!
Best Answer
The resistance in a real circuit would be far higher than the resistance of the lead wires, so the bulk of the electric field would be seen across the resistor.
Now we need to interject some reality. In a schematic, the resistor is a lumped element defined by properties at its terminals. IRL, however, it is a volume of resistive material. Two of the three dimensions of this volume are typically width, and the third is length.
If you take some fraction of that length, it will have a smaller electric field across it than the whole device does. If one side is ground, different parts will show different potentials depending on how close they are to the non-ground terminal. This is, in fact, how analog potentiometers work--the center terminal moves from one end of the fixed resistor to another, changing its potential depending on its position.
So the electric field is distributed around the circuit. The trick is that most of it is distributed across the resistive element, with very little distributed around the lead wires.