# B Redistribution of charge

#### Samanko

I know that if two conducting objects touch each other, the charges will distribute equally over the objects.
What if one object has 3 excess electrons, one is neutral?
How can the charge distribute equally over two objects?????

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#### anorlunda

Mentor
Gold Member
Two touching conductors act like a single object.

• Samanko

#### Nugatory

Mentor
That bit about how "the charges will distribute equally over the objects" applies when the number of electrons is large enough that we can treat the charge density as a continuous function instead of thinking about individual electrons. It's somewhat analogous to the way that I can talk about the smooth surface of a beach sloping evenly towards the water, even though we know that at a sufficiently small scale the beach is made up individual grains of sand - we don't know where each grain of sand is, but we know that together they arrange themselves to form a beach that we can describe as a continuous smooth surface.

Of course this approach won't work if we have just three grains of sand, and the "distribute equally" model doesn't work for three electrons either. The electrons will arrange themselves in a way that minimizes the potential energy; we'd need to know the exact shapes of the two objects to calculate what that arrangement will be.
(If you have a very large number of electrons, then doing that calculation will yield the same result as "distribute evenly"; the latter is much easier to calculate with, so that's what we use whenever it is applicable).

• Samanko

#### Mister T

Science Advisor
Gold Member
I know that if two conducting objects touch each other, the charges will distribute equally over the objects.
That's true if the objects have the same size and shape. What's the same is the electric potential.

What if one object has 3 excess electrons, one is neutral?
How can the charge distribute equally over two objects?????
It can't! The formulas assume that there are a very large number of charges. This condition is satisfied even if you have a differential element of charge $dq$! It's macroscopically small yet microscopically large.

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