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Magnetic Fields due to Electric Current — Physics STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 SciencePhysicsMagnetic Fields due to Electric Current3 Marks
Question
An electron in an atom revolves around the nucleus in an orbit of radius $0.53 \mathring A $. If the frequency of revolution of an electron is $9 \times 10^9 MHz$, calculate the equivalent magnetic moment. $\left[e=1.6 \times 10^{-19} C \right]$
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Answer

$r =0.53 \mathring A =0.53 \times 10^{-10} m$
$f =9 \times 10^9 MHz =9 \times 10^{15} Hz ,$
$e =1.6 \times 10^{-19} C$
Magnetic moment, $M _0= IA = efrr r ^2$
$=1.6 \times 10^{-19} \times 9 \times 10^{15} \times 3.142 \times\left(0.53 \times 10^{-10}\right)^2$
$=14.4 \times 3.142 \times(0.53)^2 \times 10^{-19} \times 10^{15} \times 10^{-20}$
$=1.272 \times 10^{-23} A \cdot m ^2$

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