# Doubts regarding conductors

I have some doubts regarding conductors.

1. We define conductor as the materials which have free electrons and then in their property we come to know that charge density inside the material of conductor is zero..But are not the two sentences contradictory as free electrons and the electron deficient atoms -both have charges?

2. Can we have both positive and negative charges on the surface of conductor at the same time? Griffith's book has illustrated such a picture to explain the electric field inside a conductor is zero..But should not the opposite charges cancel each other?

the way i think of conductors is the nuclei (and inner electorns) are "locked" together in a lattice and the the outer electrons flow around this lattice (free electrons means the electrons are bound to a specific atom like with a chemical bond), like a fluid. Also like how water flows to minimise the gravitational energy, the electrons 'flow' to minimise the electrical energy.

So when you have an uncharged conductor with no external electric field, there is no part of it that has a net charge. Because if there was a part of it that was say positively charged then the free electrons would flow towards it, cancelling out the charge, as it would have a lower energy. Alternately if there was a bit that was negatively charged then the free electrons would flow away from that area decreasing the charge, as it would decrease the energy.

Now if the conductor is in an external electric field, like in your image, then the free electrons would flow opposite to the direction of the electric field (the electric field is defined by the force a positive, unit charged particle). so the free electrons flow to one side of the conductor as they are 'pulled' by the electric field.

note: being 'pulled' by a force field is equal to moving to a lowest energy. (warning math) "potential energy"=$$-\frac{\Delta force}{\Delta x}$$, alternatively $$U=-\underline{ \nabla} • \underline{F}$$

This would cause a charge difference, like you have in your image, the charge difference between the two faces creates a new electric field, which is equal and oppositely directed to the external electric field, if the fields don't equal then there is still a force on the electrons, so the free electrons flow more until the fields equal, then there is no net force on the electrons.

hopefully that makes helps

• Thanks for answering ,But the charges on conductors always reside on outer surface as due to this the distance between same sign charges will be maximum. so possibly both sign of charges can't reside on conductors at the same time. Am I right? Jul 14, 2021 at 9:40
• no part of the conductor has net charge? The diagram directly contradicts that notion. Jul 14, 2021 at 10:15
• @SandipanHazra the charges will flow until the energy is at the lowest, so for a uncharged conductor the electrons are both repelled from each other but are also attracted to the positive charges in the nucleus so the electrons are dispersed around the lattice. But if extra charge is added of a conductor (like with the dome of a van de graaff generator) then it moves to maximise the distance between between them, as it has the lowest energy. so i think macroscopically, where there is no external electric field, the outer surface of a conductor has to have the same sign.
– Nyra
Jul 14, 2021 at 14:24
• @napstablook when i said that the conductor has no net charge I meant an uncharged conductor with no external electric field. In the diagram there is an electric field $E_0$ indicated by the arrow at the bottom of the diagram. I'll edit my answer to try and make it clearer.
– Nyra
Jul 14, 2021 at 14:27