Bohr around a wire

Consider an infinitely long wire made of insulating material which carries a uniform linear charge density $\lambda$. An electron is given a suitable velocity $v$ at a distance of $r$ meters from the wire such that the electron moves in a circular orbit afterwards. Find the minimum value of $r$ for which the above system is stable and the electron does not radiate.

Assumptions and Hints

• Bohr proposed that the angular momentum of an electron is quantized, so that it comes in multiples of $\hbar = h/2\pi$.
• The magnitude of $\lambda$ is equal to the magnitude of $\dfrac{\epsilon_{o}}{200\pi m_{e}e}$
• $m_{e}$ is the mass of an electron.
• $e$ is the charge of an electron.