MHT CET · Physics · Magnetic Effects of Current
An electron in a circular orbit of radius \(0.05 \mathrm{~nm}\) performs \(10^{16}\) revolution/second. What is the magnetic moment due to the rotation of electron? \(\left(\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\right)\)
- A \(3.21 \times 10^{-23}\)
- B \(2.16 \times 10^{-23}\)
- C \(3.21 \times 10^{-22}\)
- D \(1.26 \times 10^{-23}\)
Answer & Solution
Correct Answer
(D) \(1.26 \times 10^{-23}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{r}=0.05 \mathrm{~nm}=0.05 \times 10^{-9} \mathrm{~m}=5 \times 10^{-11} \mathrm{~m} \\ & \mathrm{f}=10^{16} \mathrm{r} \cdot \mathrm{p} . \mathrm{s} \\ & \mathrm{M}=\mathrm{IA}=\mathrm{ef} \pi \mathrm{r}^2 \\ & =1.6 \times 10^{-19} \times 10^{16} \times 3.14 \times\left(5 \times 10^{-11}\right)^2 \\ & =1.26 \times 10^{-23} \mathrm{~A}-\mathrm{m}^2\end{aligned}\)
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