Question:
Magnetic moment of an electron moving in a circular orbit of radius \(r\) with a speed \(v\) is
Magnetic moment of an electron moving in a circular orbit of radius \(r\) with a speed \(v\) is
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For an electron revolving in a circular orbit:
\[
\mu=\frac{evr}{2}
\]
This is one of the most important formulas in atomic physics and magnetism.
Updated On: Jun 17, 2026
- \( \dfrac{ev^2}{r} \)
- \( evr \)
- \( \dfrac{ev^2}{2r} \)
- \( \dfrac{evr}{2} \)
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The Correct Option is D
Solution and Explanation
Concept:
An electron moving in a circular orbit behaves like a current loop. The magnetic moment associated with a current carrying loop is:
\[
\mu = IA
\]
where:
• \(I\) is the equivalent current
• \(A\) is the area enclosed by the orbit
Step 1: Find the equivalent current due to revolving electron. If the electron completes one revolution in time period \(T\), then: \[ I=\frac{e}{T} \] Since: \[ T=\frac{2\pi r}{v} \] Therefore: \[ I=\frac{ev}{2\pi r} \]
Step 2: Calculate area of the circular orbit. \[ A=\pi r^2 \]
Step 3: Substitute into magnetic moment formula. \[ \mu = IA \] \[ \mu=\left(\frac{ev}{2\pi r}\right)(\pi r^2) \] \[ \mu=\frac{evr}{2} \] Hence the magnetic moment is: \[ \boxed{\frac{evr}{2}} \]
• \(I\) is the equivalent current
• \(A\) is the area enclosed by the orbit
Step 1: Find the equivalent current due to revolving electron. If the electron completes one revolution in time period \(T\), then: \[ I=\frac{e}{T} \] Since: \[ T=\frac{2\pi r}{v} \] Therefore: \[ I=\frac{ev}{2\pi r} \]
Step 2: Calculate area of the circular orbit. \[ A=\pi r^2 \]
Step 3: Substitute into magnetic moment formula. \[ \mu = IA \] \[ \mu=\left(\frac{ev}{2\pi r}\right)(\pi r^2) \] \[ \mu=\frac{evr}{2} \] Hence the magnetic moment is: \[ \boxed{\frac{evr}{2}} \]
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