Question

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

Answer 1

Hint
In the electric field, it is defined to be gradient of the potential and the surface of a conductor will have the constant potential. So, there is no electric field along the surface of the conductor, so the electrostatic field at the surface of a charged conductor is normal to the surface at any point.

Complete step by step answer
The electric field defined as the gradient of the potential and the surface of a conductor will have the constant potential. The charges which lie on the surface and around the surface of the conductor are static, so that there is no experience of the force. The force is experienced when the surface of the conductor will have some charge. Hence, the electric field is normal to the surface of the conductor.
The SI unit of the electric field is that newton per coulomb which is represented as, $N{C^{ - 1}}$, where $N$ is the newton and $C$ is the coulomb. Both these units are derived units where newton is the unit of force and the coulomb is the unit of the charge.

Note
If the component of the electric field is parallel to the surface, then the excess of the charge on the surface is forced to the accelerated motion. If the charge is set to the motion, so the conductor is not in the state of the electrostatic equilibrium. So, the electric field must be completely perpendicular to the conducting surface for the object which is in electrostatic equilibrium.