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 = \[\frac{1}{\text{ Frequency} }\]

Current in the circle, i = \[\frac{q}{t}\]

Radius of the loop, r = 0.5

\[A^\circ\] =  \[0 . 5 \times {10}^{- 10} \] m

Thus, the magnetic field at the centre due to the current in the loop is given by 

\[B = \frac{\mu_0 I}{2r}\]

\[= \frac{4\pi \times {10}^{- 7} \times \mathit{\frac{q}{T}}}{2 \times 0 . 5 \times {10}^{- 10}} \]
\[ = \frac{4\pi \times {10}^{- 7} \times 1 . 6 \times {10}^{- 19}\times 3 \times {10}^5}{2 \times 0 . 5 \times {10}^{- 10}}\]

`= (2pi xx 1.6 xx 3)/(0.5) xx 10^-11`

= 6.028 × 10^-10 ≈ 6 × 10^-10 T