# Does the electric field inside a circuit cause a potential drop with distance?

We know that when the system reaches steady-state(current does not change with time),the electric filed inside the circuit is constant. In many textbooks and lectures,professors make a graph like this one:

So,in the "wire" sections of the graph,shouldn't the potential drop due to the existance of the electric field?Because we know from electrostatics that potential drops when we move away from the point of reference.So i think the potential should drop even when there is no resistor!

Technically the resistance of a wire is never 0. Typical wires of copper have electrical conductivity of $10^{7} S/m$ at room temperature. So there is indeed a very slight potential drop but highly negligible compared to the one that would be experience at a proper resistor.
As for the problem of electrostatic, indeed from a single charged particle the field vanishes far away from this charge. Though keep in mind that in a conductor a lot of charges (around $10^{24}$ or more) are actually moving under the influence of the electric field provided by the accumulator. When steady state is reached the conductor(wire), if considered as a ideal, has organised its charge distribution so that the potential is constant on its surface which explains why there is no potential drop along the wire.