So I started off with electrostatics and everything seemed nice and mathematical and justified and then "DC circuits" happened!
I just cannot understand the model of electron flow in electrical circuits. Here are my specific doubts-:
1) If potential difference across a tiny cross section of conducting wire is zero, then why on earth does electron flow across that cross section at all? Never mind potential difference across the whole circuit.
2) Is there a constant electric field across a wire connected to a battery? If yes then how is potential difference across a zero resistance wire constant? Shouldnt it be increasing? Doesnt it violate ohms law? If no, then why do electrons flow at all?
Please take time to consider these doubts and relieve me of my frustration. I havs searched through the net for this but every answer seems like beating around the bush. All of the 4 books I have consulted do not address these facts to my satisfaction.
Frankly I think nobody understands this.
Best Answer
Consider an electron that enters your piece of wire with some velocity $v_{in}$ and emerges at the other end with a velocity $v_{out}$:
When we say the wire has a resistance what this means is that our electron will lose energy and slow down. That means we have to supply some energy to the electron to keep it moving at the same velocity. That energy is produced by generating a voltage difference $\Delta V$ between the ends of the wire. This gives the electron an energy $e\Delta V$ to replace the energy it loses to the wire.
Now suppose the wire has zero resistance. That means any electrons flowing through it don't slow down, so no extra energy needs to be added to the electrons, so the voltage difference between the ends of the wire can be zero.
This is why electrons will flow through a perfect conductor even though the potential difference is zero. The electrons have a non-zero velocity when they are pushed into the wire by whatever makes up the rest of the circuit, and they simply keep going through the wire at the same velocity.
In fact you could have a potential difference $\Delta V$ between the ends of your zero resistance wire, and what it would do is accelerate the electrons passing through it. You would in effect have built a linear accelerator. An electron would increase its energy by $e\Delta V$ on each pass through the wire. To maintain the voltage you'd need to keep pouring in power at a rate that matched the increase in kinetic energy of the electrons.