How Do Electrons Know Where to Go in a Circuit?

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Electrons in a circuit move from the negatively charged pole to the positively charged pole to restore balance, driven by an electric field. The initial electron is pushed out by the voltage difference, which acts like a force that creates a repulsive interaction among electrons, allowing them to move through the wire. This movement is akin to how objects respond to gravitational fields, with electrons following the electric field created by the battery. In a battery, reactions at the electrodes produce and consume electrons, maintaining the flow. Although electrons move slowly, the information about their movement propagates at the speed of light, enabling rapid current development throughout the circuit.
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How are electrons "pulled"?

I'm currently trying to learn about electricity, and I understand that in a circuit, the electrons will go from the negatively-charged pole to the positively-charged one in order to restore the balance. But I can't grasp how the electrons "feel" the imbalance all the way at the other end of the copper wire. What pushes the very first electron out of the negative side? How does that electron "know" where to go?

I know this is a n00bish question, but I really want to understand this!
 
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Each electron pushes against all the others without touching them like magnets that repel. This repulsive force pushes them (or pulls them) down the wire. The voltage is a measure of how hard they are being pushed in going from one to the other electrode.
 


They feel the electric field. Its similar to how a rock "knows" to fall to the center of the earth, it follows the gravitational field. Similar to this electrons follow and electric field.
 


In a battery the reaction at the positive electrode consumes electrons, the reaction at the negative electrode produces electrons. The electrons are all "connected" by the electric field, one moves, they all move. So you are pushing electrons on the wire at one end and pulling them off at the other, the information travels between the electrons at the speed of light, but the electrons themselves move much slower. So current is developed very quickly throughout the wire.
 
I'm working through something and want to make sure I understand the physics. In a system with three wave components at 120° phase separation, the total energy calculation depends on how we treat them: If coherent (add amplitudes first, then square): E = (A₁ + A₂ + A₃)² = 0 If independent (square each, then add): E = A₁² + A₂² + A₃² = 3/2 = constant In three-phase electrical systems, we treat the phases as independent — total power is sum of individual powers. In light interference...

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