Why must electrostatic fields be normal to the surface at every point of a charged conductor?

Hint: An Electrostatic field exists in the region so surrounding an electrically charged object. This charged object, when brought close proximity to an uncharged object can induce a charge on the Formidy (Formerly) neutral object. This is known as an induced charge.

Complete step by step answer:
Electric field is defined as the gradient of potential and the surface of a conductor has a constant potential. Therefore, there is no field along the surface of the conductor and hence the electrostatic field at the surface of a charged conductor should be Normal to the surface at every point.
The SI units of the electric field are Newton Per coulomb (N/C), or volts per meter (v/m). These are derived units where Newton is a unit of Force and coulomb is the unit of Charge.

Note:
Characteristic of Conductors in electrostatic equilibrium is that the electric field upon the surface of the conductor is directed entirely perpendicular to the surface.