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In the book on electrostatics and magnetism by Purcell. In the third chapter he mentions about conductors in the electrostatic field.

In the static situation there is no further motion of charge. You might be tempted to say that the electric field must then be zero within conduct- ing material. You might argue that, if the field were not zero, the mobile charge carriers would experience a force and would be thereby set in motion, and thus we would not have a static situation after all. Such an argument overlooks the possibility of other forces that may be acting on the charge carriers

He also mentions the "other forces"

There are other forces at work, however, which we may very loosely call “chemical.

So my question is what exactly are this other forces. isn't the forces only electrical?

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The gravitational forces between charges are so small that you are only left with electric forces.
The mobile electrons within a metal are often call free electrons.
They are certainly not free of all the other charges within the metal as it takes energy (work function energy) to enable them to escape from the surface.
The mobile electrons are free in that they are not under the influence of one particular nucleus which is the case for the bound electrons which are part of the metal ions making up the lattice.
The whole structure is kept together by what are called metallic bonds.
Overall what you tend to mention is the average motion of the mobile electrons in that when a static external field is applied the mobile electrons rearrange themselves into a average "steady" state in that the mean electric field within the metal is zero and there is no net drift of the mobile electrons.

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