μblog: engineering from the trenches

The semester is winding down, which means there are a lot of deadlines piling up. One of my deadlines involves re-deriving some work by Hugo Fricke regarding the electrical properties of suspensions of conducting spheres in a conducting medium. Fricke was one of the pioneers of radio-therapy and was one of the first individuals to postulate that blood cells had membranes (instead of being homogeneous solids). He did this through electrical interrogation of blood alone without using any optical techniques. I am posting my step-by-step derivations for the electric potential inside and around a single conducting sphere in a conducting medium with regards to electrostatics. I solve Laplace’s equation using separation of variables in a spherical coordinate system. Hopefully I didn’t make many errors and the rest of the derivation relating total cell conductivity and capacity will follow.

( sphere-efield.pdf ) (Image is from GNU)

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