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BITSAT 2023Paper 1
Exam
BITSAT
Year
2023
Paper
Paper 1
Subject
Physics
Chapter
Magnetic Effects of Current

BITSAT 2023 · Paper 1 · Physics · Magnetic Effects of Current

The magnetic moment of an electron (e) revolving in an orbit around...

The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by:

Options

  1. Aμ⃗L=eL⃗2m\vec{\mu}_L=\frac{e \vec{L}}{2 m}
  2. Bμ⃗L=−eL⃗2m\vec{\mu}_L=-\frac{e \vec{L}}{2 m}
  3. Cμ⃗l=−eL⃗m\vec{\mu}_l=-\frac{e \vec{L}}{m}
  4. Dμ⃗l=2eL⃗m\vec{\mu}_l=\frac{2 e \vec{L}}{m}

Correct answer

A. μ⃗L=eL⃗2m\vec{\mu}_L=\frac{e \vec{L}}{2 m}

Step-by-step solution

As M→=IA\overrightarrow{\mathrm{M}}=\mathrm{IA}
\Rightarrow|\overrightarrow{\mathrm{M}}|=\frac{\mathrm{e}}{\frac{2 \pi \mathrm{R}}{\mathrm{v}}} \pi \mathrm{R}^2\left[\because\mathrm{I}=\frac{\mathrm{Q}}{\mathrm{T}}=\frac{\mathrm{e}}{\frac{2 \pi \mathrm{R}}{\mathrm{V}}}\right]
⇒∣M⃗∣=12evR⇒∣M⃗∣=mvR1⋅e2m\Rightarrow|\vec{M}|=\frac{1}{2} e v R \Rightarrow|\vec{M}|=\frac{\mathrm{mvR}}{1} \cdot \frac{\mathrm{e}}{2 \mathrm{ m}}
⇒∣M→∣=eL2m⇒∣M→∣=−eL→2m\Rightarrow|\overrightarrow{\mathrm{M}}|=\frac{\mathrm{eL}}{2 \mathrm{ m}} \Rightarrow|\overrightarrow{\mathrm{M}}|=-\frac{\mathrm{e} \overrightarrow{\mathrm{L}}}{2 \mathrm{ m}}
[\becauseHereM→Here \overrightarrow{\mathrm{M}} and L→\overrightarrow{\mathrm{L}} will always be opposite]
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