Define Continuous Charge Distributions?

We have seen how to calculate the forces due to point charges. It may applications, however, electric forces are exerted by charged objects in the form of rods, plates, or solids. For simplicity we assume that the objects are insulators and that charge is spread throughout the surface or volume of the object, forming a continuous charge distribution.

Coulomb’s law applies only to point charges, and we therefore cannot use coulomb’s law in its point charge from to calculate the force exerted by one charged rod on the other. It is possible to imagine the rods to be covered with point charges and to use Coulomb’s law to calculate the force exerted by each point charge of one rod on each point charge of the other, but such an approach would be hopelessly complicated if the rods carry the small charge of only 1 nC, it would be necessary to consider 1010 point charges on each rod!

Instead, we return to an idea from Franklin’s time and regard the charge as a continuous property. The basic procedure is to divide the charge into infinitesimal elements and use the methods of calculus to find the total force due to all the elements.