Circular Wire Escape Velocity

A point-particle of mass $1 \, kg$ is initially at the center of a circular wire with mass $1 \, kg$ and radius $1 \, m$ . The wire is fixed in place, and the point-particle can move.

Suppose the particle starts with an initial velocity which is normal to the plane of the wire. If the only force at play is the mutual gravitation between the wire and the particle, determine the minimum initial speed required for the particle to move an infinite distance from the plane of the wire.

Details and Assumptions:
- Gravitational constant $G = 6.67 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2}$
- The wire has uniform mass density as a function of length
- Give your answer in micrometers per second $(\mu m / s)$