All Problems

Electric Current

Problem 3.159

Two long parallel wires are located in a poorly conducting medium with resistivity \(\rho\). The distance between the axes of the wires is equal to \(l\), the cross-section radius of each wire equals \(a\). In the case \(a \ll l\) find: (a) the current density at the point equally removed from the axes of the wires by a distance \(r\) if the potential difference between the wires is equal to \(V\); (b) the electric resistance of the medium per unit length of the wires.

Reveal Answer
(a) \(j=l V / 2 \rho r^{2} \ln (l / a)\) (b) \(R_{1}=(\rho / \pi) \ln (l / a)\)