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

Explanation

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 `2pi r l`. So, we have
`dR = rho (dr)/(S (r)) = rho (dr)/(2pi r l)`
and intergating between the limits, we get,
`R = (rho)/(2pi r l) In (b)/(a)`