Charge distribution along a conductor

When a conductor receives excess charge, the charge will be transferred across the entire surface of the object. 

If charge is transferred to the object at a given location, that charge is quickly distributed across the entire surface of the object. The distribution of charge is the result of electron movement. 

Since conductors allow for electrons to be transported from particle to particle, a charged object will always distribute its charge until the overall repulsive forces between excess electrons is minimized. If a charged conductor is touched to another object, the conductor can even transfer its charge to that object. The transfer of charge between objects occurs more readily if the second object is made of a conducting material. Conductors allow for charge transfer through the free movement of electrons.

Charge Distribution in a Regularly Shaped Conductor

The atoms that make up a solid object are firmly anchored in their locations. The nuclei are not free to move around throughout a solid. However, in a conductor, the electrons can move freely from one atom to another.

Adding more electrons to a solid made of conducting material can give the object an overall negative charge. 

To figure out how the new electrons will arrange themselves, we need to remember that electrons repel each other.  Since electrons are free to move on a conductor, they will move to put maximum distance between themselves. They are not able to move off the conducting solid; they are bound to the object. 

Figure 1:  Electrons will move as far as possible from one another. 

A conductor with a symmetrical shape will have a uniform charge distribution on its surface. For example, electrons on a cylinder will uniformly distribute themselves up and down its length and all around its circumference.

Charge Distribution in an Irregularly Shaped Conductor

On an irregularly shaped conductor like a teardrop-shaped conductor, the charges on the bottom of the teardrop-shaped conductor push other charges closer and closer to the tip until the charges on the tip pushes back with the same amount of force. 

At the pointed end of the conductor, the charges on the tip must be located closer together in order to be able to push back with the same force as the charges on the other end. Therefore, the charge density at a point is greater than on other areas of a conductor. The tip, though smaller, must hold its ''share'' of the charge density to balance the forces from the charge distribution on the other end.

Figure 2: In an irregular shaped conductor, more charges will be distributed where the surface curves more sharply.