Final answer:
A surface will be an equipotential surface if the potential difference across it is constant, which makes option (c) the correct answer. Equipotential surfaces are collections of points that are all at the same electric potential, and they are always perpendicular to electric field lines.
Step-by-step explanation:
A surface will be an equipotential surface if the potential difference across it is constant, which, according to the options provided, is (c) The potential difference across it is constant. An equipotential surface is defined as a collection of points that are all at the same electric potential, which means that a charge moving on this surface will not undergo any change in potential energy. As a result, no work is done by or against the electric field in moving a charge along an equipotential surface.
In addition, equipotential surfaces are always perpendicular to electric field lines. This is because the electric field is defined as the negative gradient of the electric potential, which means that the electric field points in the direction where the potential decreases most rapidly, and thus must be perpendicular to surfaces where the potential is constant.
Therefore, the correct answer to whether a surface will be an equipotential surface is (c) The potential difference across it is constant. Answer (d) It is perpendicular to the electric field lines is a true characteristic of equipotential surfaces, but it is not a defining condition. Answers (a) and (b) do not fully capture what an equipotential surface is.