I found a solution, in case anyone is curious:
The symmetry of the problem allows us to assert that we only will have even terms in our potential. So we have something of the form:
V= const + \displaystyle\sum_{\text{even }i}{a_ir^2+b_iz^2}
Hoping that the lowest order term is...
Homework Statement
I'm trying to derive Equation (1) from the paper: http://idv.sinica.edu.tw/jwang/EP101/Paul-Trap/Winter%2091%20ajp%20demo%20trapping%20dust.pdf
We are working with a cylindrically symmetric geometry along the z-axis.
r^2 = x^2 + y^2
We have electrodes described by...