Electrostatic induction in a conductor should be immpossible

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i can't grasp the idea that how is electrostatic induction possible in a conductor.

for example, if a negatively charged strip is brought near a metal conductor, the electrons will be repelled to the further end of the conductor thus making the end near the charged rod positively charged, wouldn't this mean that the flow of electrons would be restricted in the metal rod as most of them will remain at the further end of the conductor... and the delocalized electrons would no longer be free to move throughout the metallic lattice thus they would not be holding the metallic positive ions together.

As a result, i propose that the metallic conductor would collapse or atleast it melting point would decrease due to the restricted movement of delocalized electrons.

note that throughout this test, a negatively charged rod would remain near one particular end of the metal conductor.

Any help is welcome.
 
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try to put some numbers to the situation. what fraction of the freely conducting electron population would need to move before equilibrium is established?

(hint: assume that the free electron population is on the order of 10^23 per cc. assume a capacitance on the order of a pF. use Coulomb's law to figure out how many extra electrons would account for the developed charge density. i'd wager without crunching the numbers that it's on the order of 1 part in 10^15 or more. i.e. - a miniscule fraction of all the electrons are actually polarized, there is no 'depletion' of bonding electrons)