Excess electrons on a negatively charged conductor, like a sphere, are distributed uniformly on its surface due to the repulsion between like charges, which drives them to spread out. At equilibrium, the electric field inside the conductor is zero, confirming that no charge exists within it, as stated by Gauss's law. While the charge distribution is generally even, variations can occur based on the geometry, with higher charge density in areas of smaller curvature. Overall, the principle holds that excess electrons will be evenly spread across the surface of the conductor. This understanding is crucial for applications in electrostatics and conductive materials.