# Why do charges gather at the tip of any objects?

Sudheesh Singanamalla
114 Points
13 years ago

The charge on a charged conductor in equilibrium distributes such that the electric field inside the conductor vanishes and the surface potential is constant. The magnitude of the electric field on the surface is hence proportional to the charge density sigma (E ~ sigma) and its vector normal to the surface. In the special case of a sphere of radius R the electric field is constant.

Now imagine the triangle example. The corners of the triangle can be approximated locally by a small sphere of radius r. The electric field E has to be larger at the corner than in the center of each leg of the triangle, because the surface potential U is constant. This can only be achieved by a larger local charge surface density sigma at the corner.

Keep in mind, however, that a larger surface density doesn't automatically imply there are more charges in this area!

ANYWAY FUN FACTS :

1. Most of the charge on out body collects at finger tips and eyes as they are the sharp points in our body.

Hope that helps