Bohr around a wire

Consider an infinitely long wire made of insulating material which carries a uniform linear charge density λ\lambda. An electron is given a suitable velocity vv at a distance of rr meters from the wire such that the electron moves in a circular orbit afterwards. Find the minimum value of rr 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 =h/2π\hbar = h/2\pi.
  • The magnitude of λ\lambda is equal to the magnitude of ϵo200πmee\dfrac{\epsilon_{o}}{200\pi m_{e}e}
  • mem_{e} is the mass of an electron.
  • ee is the charge of an electron.
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