Final answer:
Only one electric-field line can exist at any point in space, and thus only one field configuration is possible for a given potential. The potential difference and electric-field strength are directly related in a constant electric field, with potential difference being proportional to the product of field strength and distance.
Step-by-step explanation:
The concept of electric potential is closely tied to the behavior of electric fields. To address the question of whether two different electric fields can exist for the same potential: technically, electric fields are vectors, and at any given point in space, they have a single, uniquely defined direction and magnitude. Hence, only a single electric-field line can exist at any given point in space, implying that for a given potential, there can be only one electric field configuration at that point.
For the related questions, when two charges lie along the x-axis, the net electric field will vanish at some point along that axis (apart from at infinity). This is because electric fields are vectors and can cancel each other out when their magnitudes are equal and opposite at a point in space.
Regarding the potential difference and electric-field strength, for a constant electric field, the potential difference is directly proportional to the electric-field strength and the distance over which the field is applied. The potential difference is calculated by integrating the electric field over the distance between the two points.