Question

In the Bohr model of hydrogen atom, the electron circulates around the nucleus in a path of radius $5.1\times {10}^{-11}m$ at a frequency $6.8\times {10}^{15}{s}^{-1}$. Find the magnetic field set up at the centre of the orbit.

Answer 1

The circulating electron is equivalent to a circular current carrying loop,

$i=ef$

$=6.8\times {10}^{15}\times 1.6\times {10}^{-19}$

$=1.08\times {10}^{-23}amp$

Magnetic field at the center

$B=\frac{{\mu }_{0}i}{2a}=\frac{4\pi \times {10}^{-7}\times 1.08\times {10}^{-3}}{2\times 5.1\times {10}^{-11}}$

$=13.3weber/m^2$