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.

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