Escaping the magnetic field of a wire

From the surface of a cylindrical wire of radius $R=1~\textrm{cm}$ carrying a current $I= 1~\textrm{mA}$ an electron escapes with velocity $v_{0}=30~\textrm{m/s}$ perpendicular to the surface of the wire. What will be the electron's maximum distance in meters from the axis of the wire?

Details and assumptions

$\frac{\mu_{0}}{4\pi}= 10^{-7}~\textrm{H/m}$ $e/m_{e}=1.76 \times 10^{11}~\textrm{C/kg}$