(A): Potential everywhere on a conducting surface of infinite extent i...
Statement A: "Potential everywhere on a conducting surface of infinite extent is zero."
Statement R: "Displacement density on a conducting surface is normal to the surface."
Statement A is true. According to the properties of conductors, the electric potential on the surface of a conductor in electrostatic equilibrium is constant and has the same value throughout the surface. In the case of a conducting surface of infinite extent, this potential is generally considered to be zero.
Statement R is also true. The displacement density, also known as the electric flux density or electric displacement field, is a vector quantity that describes the amount of electric flux passing through a surface per unit area. On a conducting surface, the displacement density is normal (perpendicular) to the surface. This is due to the fact that in electrostatic equilibrium, charges accumulate on the surface of the conductor, and the electric field inside the conductor is zero. As a result, the displacement density is directed perpendicular to the surface.
However, Statement R does not provide a correct explanation of Statement A. While Statement R is true, it does not directly explain why the potential on a conducting surface of infinite extent is zero. The zero potential on a conducting surface is a result of the properties of conductors and the distribution of charges in electrostatic equilibrium.
Therefore, the correct answer is B: Both A and R are true, but R is not a correct explanation of A.