In physics class my teacher is indicating that the electric potential in a wire remains constant until a resistor occurs. If the electrons in the wire are moving away from the negative terminal of the battery and $V = kQ/r,$ how can this be true? The electric potential in the battery would seem to drop in magnitude as the electrons got farther from the terminal. Please help!
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It's correct to say that V=kQ/r but just speaking about an electric field generated in the space by a point charge valued as Q. In circuits you have just to think about "energy and work" of the points regardless of their distance from the battery poles: in the ideal wires you have no "friction" (resistance) in the flow of the charge column inside the wire, so all the energy is naturally spent to "press" that column through the resistors. In actual wires you have a small friction, the longer the wire the stronger the total friction (resistance of a wire), the ticker the wire the weaker the total friction.
