Calculating a Non-Uniform Electric Field Given 6 different Electrode Pairs

[penguino6971]

Homework Statement

I have been asked to find the most non-uniform electric field generated by the electrode pairs below given a range of frequencies, voltages, and distances between the electrode pairs. I intend to use a program such as Matlab to run various frequencies, distances, and voltages and then graphing the results to see the most non-uniform electric field. However, due to the unique design of the electrode pairs, I have no idea on where to start and how frequency relates to the electric field.

Relevant Equations

V = E*d

I know how to find the electric field of more traditional designs i.e. a sphere, through Gauss' Law but I don't think Gauss' Law applies to this scenario. I tried to separate each part of the electrode into simple spheres and rods and using Gauss' Law to find these individual elements. This proved to inefficient and could be very much incorrect. Any help would be appreciated.

 

[Nate810]

If you can't make use of Gauss' law for this problem, then you may need to resort to solving the Laplace equation, which will give you the electric potential. From this, you can then calculate the electric field using the gradient of the electric potential. Note that this will require boundary conditions, and a numerical solution is likely the only approach that can be taken.