A very long straight wire in a vacuum carries a steady current of $20\ \text{A}$. An electron is at a distance of $1.5\ \text{cm}$ from the wire, as in the figure. It is moving straight away from the wire, at right angles to it, with a speed of $5.0 \times 10^{5}\ \text{m/s}$. The only force on it is the magnetic force of the wire's field. Gravity is negligible, and so is any radiation. Take $m_e = 9.11 \times 10^{-31}\ \text{kg}$, $e = 1.60 \times 10^{-19}\ \text{C}$ and $\mu_0 = 4\pi \times 10^{-7}\ \text{T m/A}$. The electron curves as it moves out. What is the greatest distance from the wire that it reaches? Give the answer in $\text{cm}$, to two decimal places.

Fig. 1: A long straight vertical wire carries 20 A upwards. Crosses to its right show its magnetic field going into the page there. An electron 1.5 cm to the right of the wire has an arrow pointing straight away from the wire, for its speed of 5.0 times 10 to the 5 metres per second.