# 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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