Given below are two statements.
Statement I: Electric potential is constant within and at the surface of each conductor.
Statement II: Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point.
In the light of the above statements, choose the most appropriate answer from the options given below.

We consider each statement about conductors in electrostatic equilibrium.

Statement I: In electrostatic equilibrium, the electric field inside a conductor is zero. Since $$\vec{E} = -\nabla V$$, a zero electric field throughout the conductor means the potential does not change — it is constant within and on the surface of the conductor. This statement is correct.

Statement II: For a charged conductor in equilibrium, any net charge resides on the surface. The electric field just outside the surface must be perpendicular to the surface at every point. If there were a tangential component, it would cause surface charges to move, contradicting the assumption of electrostatic equilibrium. Therefore, the field is purely normal (perpendicular) to the surface. This statement is correct.

Since both statements are correct, hence the correct answer is Option A.