Final answer:
The total electric potential due to two charges on the x-axis is equal to zero at points where the contributions of the individual charges cancel out. These points typically lie symmetrically around the midpoint between two equal and opposite charges.
Step-by-step explanation:
The question is related to the electric potential due to a system of point charges. Electric potential (V), by definition, decreases with distance from a point charge, while the electric field (E) decreases with the distance squared. If the potential at infinity is taken to be zero, we look for points other than at infinity where the total electric potential due to two charges along the x-axis is also zero.
As per the principles of electromagnetism, there could exist points along the x-axis where the contributions to the electric potential by two charges can cancel each other out, making the net electric potential zero. Without specific details about the charges' values and positions, we can conjecture that these points would symmetrically lie on either side of the midpoint between two equal and opposite charges. To find these points mathematically, one would set up an equation where the sum of the potentials from both charges at a point x equals zero and solve for x.
Note that if the question entails a specific answer (x=2a), it would require the specifics of the charge placement and values to verify that answer. This problem underscores the significance of the potential being a scalar quantity, making it simpler to work with compared to vector quantities such as the electric field.