Cylinder and Stripe Monopolar Sources

Here L is not the cylinder length because that is infinite L is the length of a cylinder segment. The radius of the half-immersed cylinder is a, and r is the radius of a chosen outside concentric hemicylinder in the tissue volume. R is the resistance between two cylinders and in contrast to the sphere, R diverges if r oo. 

The surface of a cylinder segment is 27rrL, and if I is the current fed into that cylinder segment the current density in tissue is  

It is not possible to define a finite potential at r = oo because a certain current I then results in an infinite potential because R diverges. With an infinitely long cylinder, only potential differences can be defined and Eq. (6.24) describes a quantity often called the logarithmic potential for this difference between two points at distance ri and t2  

Because the current density field has no changes in the axial direction, the calculations are simplified to 2D problems. Around the ends of a finite length rod in an infinite conductive medium, the problem is no longer 2D, and the best analytical approach is to turn to an ellipsoid geometry (see following section on finite length rod). 

The two parallel-cylinder solution (section 6.3.2) is directly applicable to a complete cylinder discussed previously (e.g., with an infinite metal plate), because the current density field is unchanged if the isoelectric plane surface is covered by a thin metal sheet. The resistance is halved and the conductance doubled (see Eq. (6.26))  

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