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

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

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