Why does charge on a pointy conductor not uniformly spread?

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SUMMARY

When charge is placed on a conical conductor, it does not distribute uniformly due to the geometric properties of the surface. Unlike a spherical conductor where charge spreads evenly, the charge density on a conical conductor is higher near the tip due to the reduced surface area at that point. This phenomenon occurs because the motion of electrons in conductors is fluid, leading to a concentration of charge where the surface area is smaller.

PREREQUISITES
  • Understanding of electrostatics and charge distribution
  • Familiarity with the properties of conductors
  • Basic knowledge of geometry related to surface area
  • Concept of electric field and potential
NEXT STEPS
  • Study the principles of charge distribution on different geometries, focusing on conical and spherical shapes
  • Learn about the mathematical derivation of electric field strength near pointed conductors
  • Explore the concept of surface charge density and its implications in electrostatics
  • Investigate the effects of conductor shape on electric potential and field lines
USEFUL FOR

Students of physics, particularly those studying electrostatics, as well as educators and anyone interested in the behavior of electric charges on various conductor shapes.

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Homework Statement


If charged is place on a spherical conductor, it distributes uniformly. If charged is placed on a conical conductor, it does not spread uniformly.

Homework Equations


Remember that, in a conductor, the motion of electrons is fluid.

The Attempt at a Solution


Taking the given example, a cone, if we placed charge on it, charge would spread. It would spread in the sense that every square centimeter would have a constant charge. Because surface area clumps near the cone's tip, however, charge would be more concentrated there.

I get the impression that this attempt is bogus. I don't see why a surface's surface area is greater at a vertex than on a flat plane.
 
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Why do they distribute at all?
 

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