NON-Gauss Problem: Find Electric Potential for Charged Sticks

Charged objects in real life generally are not in the 3 shapes we need for Gauss's law - spheres, long cylinders, or large plates.  Here, we look at how to set up the integrals necessary for finding the electric potential of charges sticks at arbitrary locations from the stick, where we do not have much in the way of symmetry to help simplify life.

The concept behind it is to break the problem into point charges.  The only thing we know exactly in electrostatics is how to deal with point charges, with E = kQ/r^2 and V = kQ/r.  So we need to break into point charges, find the small contributions from each charge, and add them all up, or integrate.  The one other piece of this so it works is to use a ratio of charge to length.  This allows for a substitution into the integral to make it solvable.

This video has two examples of sticks and finding electric potential.  I hope it helps!