Physics

The key insight is that zero net force occurs where the electric forces from both charges cancel—which happens when the test charge sits at a point where the two charges exert equal-magnitude forces in opposite directions. Since both charges are positive, this balance point must lie on the line between them, closer to the weaker charge. Set up the force-balance equation using Coulomb's law: the magnitudes of the two forces must be equal, then solve for the distance from the $+6\,\mu\text{C}$ charge.

The key insight is that zero net force occurs where the electric forces from both charges cancel—which happens when the test charge sits at a point where the two charges exert equal-magnitude forces in opposite directions. Since both charges are positive, this balance point must lie on the line between them, closer to the weaker charge. Set up the force-balance equation using Coulomb's law: the magnitudes of the two forces must be equal, then solve for the distance from the $+6\,\mu\text{C}$ charge.