Physics - Modern Physics Question with Solution | TestHub

To keep the electron in its orbit, the centripetal force on the electron must be equal to the electrostatic force of attraction,According to Bohr's angular momentum quantization condition: $\Rightarrow \pi rm{e}^2={\epsilon }_0{h}^2$ $r=\frac{{\epsilon }_0{h}^2}{\pi m{e}^2}---(3)$ From (ii) and (iii), we have $v=\frac{h\pi m{e}^2}{2\pi m{\epsilon }_0{h}^2}=\frac{e^2}{2{\epsilon }_{0}h}$ The magnetic field at the center of the circular loop is given by, $B=\frac{{\mu }_{0}I}{2r}$ where, current $I=\frac{\mathrm{q}}{\mathrm{T}}$ and time $T=\frac{2\pi r}{v}$ $\therefore I=\frac{ev}{2\pi r}$Using, equations (2), (3) and (4) we have, $B=\frac{{\mu }_0{e}^7\pi m^2}{8{\epsilon }_0^3{h}^5}$