Physics
Physics
Problem
A student sketches the equipotential map for two point charges of equal magnitude but opposite sign separated by along the -axis. In the sketch, each charge is surrounded by perfect concentric circles that do not distort or merge as they extend into the space between the charges. Which statement best explains why this sketch cannot represent the actual equipotential distribution? a) Concentric circles would indicate both charges have the same sign; since one charge is negative, no closed equipotential circles can surround it. b) Because the equal and opposite charges cancel each other's potential everywhere between them, the entire space between the charges is one equipotential surface, so no equipotential lines should be drawn there. c) The sketch ignores that potentials from the two charges add, so points equidistant from one charge are at different potentials depending on their distance from the other charge. d) Equipotential lines for two point charges must be straight lines that run between the charges, so curved circles cannot be correct.Intuitive explanation
The key insight is that equipotentials must be perpendicular to electric field lines everywhere, and field lines from opposite charges behave very differently than from like charges. Between a positive and negative charge, the field lines connect directly from one to the other, forcing equipotentials to curve and pinch inward in the middle region—they cannot remain as independent concentric circles around each charge. A sketch showing perfect circles around both charges ignores this fundamental constraint of how fields superpose.
Intuitive explanation
The key insight is that equipotentials must be perpendicular to electric field lines everywhere, and field lines from opposite charges behave very differently than from like charges. Between a positive and negative charge, the field lines connect directly from one to the other, forcing equipotentials to curve and pinch inward in the middle region—they cannot remain as independent concentric circles around each charge. A sketch showing perfect circles around both charges ignores this fundamental constraint of how fields superpose.