why most electrostatic field be normal to the surface at every point of a charged conduction?
Characteristic of conductors at electrostatic equilibrium is that the electric field upon the surface of the conductor is directed entirely perpendicular to the surface. There cannot be a component of electric field (or electric force) that is parallel to the surface.
If the conducting object is spherical, then this means that the perpendicular electric field vectors are aligned with the center of the sphere. If the object is irregularly shaped, then the electric field vector at any location is perpendicular to a tangent line drawn to the surface at that location.
The motion of electrons, like any physical object, is governed by Newton’s laws. One outcome of Newton’s laws states that unbalanced forces cause objects to accelerate in the direction of the unbalanced force and a balance of forces causes objects to remain at equilibrium
If there were a component of electric field directed parallel to the surface, then the excess charge on the surface would be forced into accelerated motion by this component. If a charge is set into motion, then the conductor is not in a state of electrostatic equilibrium. Therefore, the electric field must be entirely perpendicular to the conducting surface for objects that are at electrostatic equilibrium.
Certainly a conducting object that has recently acquired an excess charge has a component of electric field parallel to the surface; it is this component that acts upon the newly acquired excess charge to distribute the excess charge over the surface and establish electrostatic equilibrium. But once reached, there is no longer any parallel component of electric field and no longer any motion of excess charge.
