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

The electrostatic field at the surface of a charged conductor must be normal (perpendicular) to the surface at every point due to the following reasons:

1. Static Condition: In a static situation, the charges in a conductor are at rest. If the electric field were not perpendicular to the surface, it would have a component along the surface of the conductor. This tangential component of the electric field would exert a force on the free charges causing them to move, which contradicts the assumption of electrostatics.

2. Charge Redistribution: When a conductor is charged, the excess charge resides on the outer surface and redistributes itself in such a way that the electric field inside the conductor is zero. This is possible only if the electric field at the surface is perpendicular to it. If there were a component of the electric field parallel to the surface, it would give rise to a non-zero electric field inside the conductor, which contradicts the property of a conductor in electrostatic equilibrium.

3. Gauss's Law: According to Gauss's law, the electric field through a closed surface is proportional to the charge enclosed by the surface. If the electric field were not normal to the surface, then there would be a net flux through the surface, implying a net charge inside the conductor, which contradicts the fact that the net charge in a conductor resides on its surface.

Therefore, the electrostatic field at the surface of a charged conductor is always normal to the surface at every point.