On an irregularly shaped conductor, where does charge tend to accumulate?

On an irregularly shaped conductor, where does charge tend to accumulate?

• A. Flat parts of the surface
• B. Areas with the smallest radius of curvature
• C. Uniform charge distribution
• D. Areas with the largest radius of curvature

Answer: (B)

On a conductor, charges move until they reach electrostatic equilibrium and reside on the surface. The amount of charge per unit area, sigma, is tied to the electric field just outside the surface by E_out = sigma/epsilon0, and the field lines must meet the surface perpendicularly. At a point where the surface curves sharply (small radius of curvature), these field lines crowd together, making the local electric field stronger. To satisfy the boundary condition and the energy distribution, more charges accumulate in that region, increasing sigma there. In contrast, smoother or flatter areas (large radius of curvature) spread charge over a larger area, giving a smaller sigma. So charges congregate where the curvature is greatest, i.e., areas with the smallest radius of curvature.

On a conductor, charges move until they reach electrostatic equilibrium and reside on the surface. The amount of charge per unit area, sigma, is tied to the electric field just outside the surface by E_out = sigma/epsilon0, and the field lines must meet the surface perpendicularly. At a point where the surface curves sharply (small radius of curvature), these field lines crowd together, making the local electric field stronger. To satisfy the boundary condition and the energy distribution, more charges accumulate in that region, increasing sigma there. In contrast, smoother or flatter areas (large radius of curvature) spread charge over a larger area, giving a smaller sigma. So charges congregate where the curvature is greatest, i.e., areas with the smallest radius of curvature.