Magnetic Moment Calculator
Free calculate electron and atomic magnetic moments from spin and orbital angular momentum. Get instant, accurate results with our easy-to-use calculator.
Input Parameters
For electron: s = ½
Results
Enter parameters to calculate
What is Magnetic Moment?
Magnetic moment (μ) is a vector quantity that characterizes the magnetic strength and orientation of a magnetic dipole, such as an electron, atom, or current loop. It determines how the system interacts with external magnetic fields.
For electrons, magnetic moment arises from two sources: orbital angular momentum (electron motion around nucleus) and spin angular momentum (intrinsic electron spin). The total moment is the vector sum of both contributions.
Magnetic moments are quantized in quantum mechanics and are typically expressed in units of the Bohr magneton (μ_B = eℏ/(2m_e) ≈ 9.274×10⁻²⁴ J/T), which is the natural unit for atomic magnetic moments.
Magnetic Moment Formulas
Spin Moment
Orbital Moment
Where: μ_B = 9.274×10⁻²⁴ J/T (Bohr magneton), g_s ≈ 2.0023 (g-factor), s = spin quantum number, l = orbital quantum number
How to Calculate
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1
Determine quantum numbers
For electron: spin s = ½, orbital l = 0, 1, 2, ... depending on orbital type.
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2
Calculate spin moment
μ_s = g_s × μ_B × √(s(s+1)) where g_s ≈ 2.0023 for electron.
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3
Calculate orbital moment
μ_l = μ_B × √(l(l+1)) for orbital angular momentum contribution.
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4
Calculate total moment
μ_total = √(μ_s² + μ_l²) (vector sum, simplified for perpendicular components).
Practical Examples
Example 1: Electron Spin Moment
Electron with s = ½. Calculate spin magnetic moment.
Solution:
μ_s = 2.0023 × 9.274×10⁻²⁴ × √(0.5×1.5)
μ_s ≈ 9.285×10⁻²⁴ J/T ≈ 1.001 μ_B
Example 2: Orbital Moment
Electron in p orbital (l = 1).
Solution:
μ_l = 9.274×10⁻²⁴ × √(1×2)
μ_l ≈ 1.311×10⁻²³ J/T ≈ 1.414 μ_B
Applications
Atomic Physics
Understanding atomic structure, analyzing magnetic properties of atoms, and studying electron configurations.
Magnetic Materials
Characterizing ferromagnetic, paramagnetic, and diamagnetic materials based on atomic magnetic moments.
Spectroscopy
Understanding Zeeman effect, analyzing magnetic resonance, and interpreting atomic spectra.
Education
Teaching quantum mechanics, understanding electron properties, and learning about atomic magnetism.
Frequently Asked Questions
What is the Bohr magneton?
The Bohr magneton (μ_B = eℏ/(2m_e) ≈ 9.274×10⁻²⁴ J/T) is the natural unit for atomic magnetic moments. It represents the magnetic moment due to one unit of angular momentum (ℏ).
Why is the g-factor approximately 2 for electrons?
The electron spin g-factor g_s ≈ 2.0023 comes from quantum electrodynamics. The deviation from exactly 2 is due to quantum corrections. For most calculations, g_s = 2 is a good approximation.
How do orbital and spin moments combine?
They combine vectorially: μ_total = μ_l + μ_s. The magnitude depends on the angle between them. For parallel: μ = μ_l + μ_s. For antiparallel: μ = |μ_l - μ_s|.
What is the difference from current loop moment?
Current loop: μ = NIA (macroscopic). Atomic moment: quantum mechanical, quantized, involves spin and orbital angular momentum. Both are magnetic dipoles but on different scales.
How does this relate to magnetic susceptibility?
Materials with unpaired electrons (net magnetic moment) are paramagnetic. Materials with paired electrons (zero net moment) are diamagnetic. Total atomic moments determine material's magnetic properties.