Question

An electron makes 3 × 10⁵ revolutions per second in a circle of radius 0.5 angstrom. Find the magnetic field B at the centre of the circle.

Answer 1

Given:
Frequency of the electron = 3 × 10⁵
Time taken by the electron to complete one revolution, T = $\frac{1}{\mathrm{Frequency}}$
Current in the circle, i = $\frac{q}{t}$
Radius of the loop, r = 0.5 ${\mathrm{A}}^{°}$ = $0.5\times {10}^{-10}\mathrm{m}$
Thus, the magnetic field at the centre due to the current in the loop is given by
$B=\frac{{\mathrm{\mu }}_{0}I}{2r}$
$$\begin{gathered} =\frac{4\mathrm{\pi }\times {10}^{-7}\times {\displaystyle \frac{q}{T}}}{2\times 0.5\times {10}^{-10}} \\ =\frac{4\mathrm{\pi }\times {10}^{-7}\times {\displaystyle 1.6\times {10}^{-19}}}{2\times 0.5\times {10}^{-10}\times 3\times {10}^5} \\ =6\times {10}^{-10}\mathrm{T} \end{gathered}$$