(a) Study the nature of the velocity field arising from a pair of parallel vortex lines, with \(s_{1}=\) +1 and \(s_{2}=-1\), separated by a distance \(d\). Derive and discuss the general equation of the stream lines.

(b) Again, using Fetter's analytical approximation for the functions \(f\left(ho_{1}^{\prime}\right)\) and \(f\left(ho_{2}^{\prime}\right)\), calculate the energy (per unit length) of the system and show that its limiting value, as \(d \rightarrow 0\), is \(11 \pi \hbar^{2} n_{0} / 12 m\). Making use of this result, derive expression (11.6.8) for the critical velocity of superflow.