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Assume we are working with a postive test charge : In an electrochemical cell work is done by the chemical reactions to move a positive test charge from the negative terminal to the positive terminal , this results in the positive test charge gaining electrical potential energy . Hence when connected to an external circuit the positive test charge would move to the negative terminal via the conducting wires . My question is why doesnt the positive test charge just move in the battery back towards the negative terminal , why must it move along the conducting pathway ? Another question that troubles me is that while the test charge was moving along the conducting pathway it's potential energy was being converted to kinetic energy , hence why do we assume that potential energy is only being consumed within the circuit elements such as a light bulb , why don't we take into account the potential energy being converted into kinetic energy when the test charge moves through the conducting wires ?

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why doesnt the positive test charge just move in the battery back towards the negative terminal , why must it move along the conducting pathway

The conductive mechanism is different in metallic wires compared to in the electrolytic liquid content of a battery (called an electrolyte).

In metals, the charge flow (current) is due to electrons flowing, while in electrolytes it is due to ions flowing. Electrons do not flow through an electrolyte - it is not an electron conductor, but an ionic conductor. Rather, electrons are resting in the neutral atoms that then give up their valence electron to the metallic electrode, when it reaches it. The atom split from it's electron (or vice versa, gaining an extra electron) is then called an ion and has a net charge due to the lack (or gain) of electronic negative charge.

So, this is why electrons do not flow through the battery content. It is simply not conductive for electrons. The question now is: why would an atom ever give up (or gain) it's electron?

As you started out saying, chemical reactions move charges to higher potential. What you actually mean is that chemical reactions take place between the atoms in the electrolyte and the electrode when in contact. Those chemical reactions, being oxidation or reduction, set up a chemical potential that is stronger than the electric potential achieved by the charges being moved. The exact mechanism can be very detailed chemically and depend on the exact species and their polarization etc.

The chemical potential is therefore the driving factor and it must naturally be stronger than the electric repulsion between electrons. Only then can the battery "move" electrons to the battery terminal and accumulate or "pack" them there against their will, giving that terminal a fixed net charge. The mechanics of the electrolyte and the continued reactions happening are holding back the ions from recombining with (delivering back) the electron. When an external circuit then is attached, another and more accepting path is given to the electron and it starts moving.

Another question that troubles me is that while the test charge was moving along the conducting pathway it's potential energy was being converted to kinetic energy , hence why do we assume that potential energy is only being consumed within the circuit elements such as a light bulb , why don't we take into account the potential energy being converted into kinetic energy when the test charge moves through the conducting wires ?

This really is a new question and would be better in a new post to avoid this answer being far too long - but here goes...

Yes, the potential energy is spent while speeding up the electron. True. In the same way the gravitational potential energy is spent speeding up the falling skydiver.

But soon the skydiver starts reaching a steady speed. The air resistance brakes his acceleration and soon balances out the gravitational pull. Then he falls at constant speed (called terminal velocity in this specific case). But he still falls. He gains no more kinetic energy, but the potential energy still decreases the closer he comes to the ground.

The same is the case for electric current. Yes, electric potential energy is spent speeding up the charges. But very soon they reach a steady state, a constant speed. A constant and steady current. It happens very fast in usual real-life circuits. Since the battery potential difference is not depleted yet, although some of it's "push" has been spent speeding up the electrons, it continues to "push".

Were does this energy go? Where does the lost potential energy disappear to for the skydiver and for the electron? To answer that we should ask the question: What holds them back?

  • The skydiver is held back by air resistance / drag. This "friction" with the air and motion of the air, while he pushes it away, absorbs the potential energy (the air molecules are heated up and set in motion).
  • The electron is held back by electronic resistances in the circuit. Places where the electrons at "struggling" to pass. There might be a tiny resistance in the wires themselves, although often negligible so the resistance is always concentrated at the components in the circuit, such as at actual resistors.

Were their no resistors and thus no resistance in a circuit, then the electrons would never be slowed down. They would speed up constantly (until the wire resistances become significant enough and the wires might burn out), just like the skydiver would speed up constantly if there was no air to provide drag.

I hope this answers your questions.

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