Question

A homogeneous poorly conducting medium of resistivity ρ fills up the space between two thin coaxial ideally conducting cylinders. The radii of the cylinders are equal to a and b, with a <b, the length of each cylinder is l. Neglecting the edge effects, find the resistance of the medium between the cylinders.

Answer 1

Let us mentally isolate a thin cylindrical layer of inner and outer radii r and r + dr respectively. As lines of current at all the points of this layer are perpendicular to it, such a layer can be treated as a cylindrical conductor of thickness dr and cross-sectional area 2πrl. So, we have,

and integrating between the limits, we get,