All Problems Electric Current
Problem 3.169
A long round conductor of cross-sectional area \(S\) is made of material whose resistivity depends only on a distance \(r\) from the axis of the conductor as \(\rho=\alpha / r^{2},\) where \(\alpha\) is a constant. Find: (a) the resistance per unit length of such a conductor; (b) the electric field strength in the conductor due to which a current \(I\) flows through it.
(a) \(R_{1}=2 \pi \alpha / S^{2}\) (b) \(E=2 \pi \alpha I / S^{2}\).