All Problems

Electric Current

Problem 3.159

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

Reveal Answer
(a) j=lV/2ρr2ln(l/a)j=l V / 2 \rho r^{2} \ln (l / a) (b) R1=(ρ/π)ln(l/a)R_{1}=(\rho / \pi) \ln (l / a)