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On an irregularly shaped conductor, the surface charge density is greater at locations where the radius of curvature is smallest due to the electric field created by the surface charges. According to Gauss's law, the electric field strength is inversely proportional to the radius of curvature; sharper points or edges (smaller radius) produce a stronger electric field. To maintain electrostatic equilibrium, this results in a higher concentration of charge at these points, leading to greater surface charge density where the curvature is smallest. Thus, the distribution of charge is not uniform, reflecting the geometry of the conductor.

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