Question

why most electrostatic field be normal to the surface at every point of a charged conductor

Answer 1

if E was not normal to the surface , it would have some non -zero component along the surface. Free charges on the surface of conductor would then experience force and move. In the static situation , therefore E should have no tangential component . thus electrostatic field must be normal to the surface of charged conductor at every point.
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Answer 2

Answer:

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Explanation:

So that tangent on charged conductor gives the direction of the electric field at that point.