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Upon reading matter and interactions ,In the chapter "electric field in a circuit" and surface charge distributions in a steady current, The book dosen't explain why doesn't the surface charges move in direction of their electric field .

More over the author of the book awnsered a question like this one on this forum and here's his awnser

Note too that even if the surface charges are mobile, the surface charge density at any location on the surface in the steady state does not change, so the field contributed by the surface charges doesn't change

How is that true i am still confused by his furher awnsers here is the link of the OP Distribution of surface charges in an electric circuit

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Electrons on the surface do move, but their density is constant because as N electrons leave some area of a conductor, another N electrons come to that area from the other side.

Analogy: when water particles move down the river, they are replaced with particles from up the river. So particles change, but their number stays the same.

This is what the "steady state" that you mentioned refers to. If there's no electricity - the state is steady and that's probably clear. But when they move - if the rate at which they leave is the same as the rate at which new electrons arrive - that's also a steady state.

If you find electricity complicated, you may want to watch Prof. Carlson lectures, they are pretty simple.

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The surface charges do move, however for every charge moved there's another charge taking its place.. Hence the charge density is constant for a particular conductor

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