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Source of image: Fundamentals of Physics extended fifth edition by Halliday, Resnick and Walker. Concerned to First Paragraph.

Why in the rejected scheme, Spheres are supposed to go neutral (or become discharged) when connected to a conductor?

Just after that is written ", bringing them quickly to the same potential." I do not understand what author is trying to say. Does he mean that electrons, first, would move to the negative terminal and would cancel its charge (making this terminal neutral) and then make this terminal positively charged so that both the given terminals become positive (reach to same potential)? Is that what he is trying to say?

If this is what he is trying to deliver, I have trouble. Because, I can not understand what kind of spheres he is talking about. What does he exactly mean by "conducting spheres"? I am taking it as a normal sphere which is already somewhat filled with charge carriers before being connected to the conductor but I really doubt if I am right.

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A conducting sphere is a sphere made of a material which conducts electricity. So think of it as a metal sphere.

If you have a conducting sphere which is positively charged and one which is negatively charged then there is a potential difference between them with the positively charged sphere being at a higher potential.

There are also electric field lines going from the positively charged sphere to the negatively charged sphere.

However charges cannot move from one sphere to the other sphere because they are separated by an insulator (air) which is a material which has no mobile charge carriers.

When a resistor, which contains mobile charge carriers (electrons), is connected between the spheres the mobile charge carrier feel the force due to the electric field in the resistor and start to move.

Electrons move from the negatively charged sphere which has a surplus of electrons to the positively charged sphere which has a deficit of electrons. So the negatively charged sphere is losing electrons and so its potential is becoming less negative and the positively charged sphere is gaining electrons and so it's potential is becoming less positive.

Eventually there is no potential difference between the spheres and so no electric field inside the resistor and so the flow of electrons (electric current) ceases.

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