Continuous Charge Distributions

Learning Goals

Continuous Charge Distributions

If many charges are distributed in space in a continuous distribution, then one approach is to treat infinitesimal charge elements as point charges, and use Coulomb’s law to find the corresponding infinitesimal vector element of electric field:

This equation is really shorthand for up to three different integrals which sum the components of the vector integrand along individual coordinate directions. It is often possible (and important) to utilize symmetry arguments to determine which of these integrals are nonzero without explicitly performing the integration.

The Coulomb approach outlined here is not the only way to determine electric fields due to extended continuous charge distributions. In later chapters, you will learn about two more techniques which are often easier to implement: Gauss’s law and electric potential.