A very long, thin straight wire carries a uniform positive charge per unit length $\lambda$. An electron moves round the wire in a circle of radius $2.0\ \text{cm}$, in a plane at right angles to the wire, with a steady speed of $4.0 \times 10^{6}\ \text{m/s}$. The wire is far from all other charges. The electron is held in its orbit by the electric force alone; neglect gravity and any magnetic effects. Take $\dfrac{1}{4\pi\varepsilon_0} = 9.0 \times 10^{9}\ \text{N m}^2\,\text{C}^{-2}$, $e = 1.60 \times 10^{-19}\ \text{C}$ and $m_e = 9.11 \times 10^{-31}\ \text{kg}$. What is $\lambda$? Give the answer in $\text{nC/m}$, to two decimal places.