Continuous Charge Distribution

A continuous charge distribution is a collection of infinite point charges spread throughout a body.

Infinite?

Okay, technically we can’t have infinite point charges in a finite object, but because there’s just so many point charges, we treat the entire object as continuous. It makes things easier

The body may be uniform (where the charges are evenly spread out) or non-uniform. These charge distributions can further be categorized based on the shape of the body. Due to the infinite nature of such distributions, we need to use integration techniques with Coulomb’s Law to obtain the forces from them.

It is very, very very important to remember that a continuous charge distribution is a hypothetical set of point charges, and is different from a charged object. We can have a charged conducting sphere, for example, but due to the dissipation of charges, such an object cannot have a volume charge density (i.e. $\rho =0$), and only a surface charge density. However, we can have a 3-dimensional charge distribution such that $\rho >0$.

Charge Density §

Some examples of continuous charge distributions:

• Infinite Line of Charge
• Ring of Charge
• Plane of Charge
• Charged Cylinder with Infinite Length