Free Spin Magnetic Moment Calculator
Calculate the magnetic moment of a spinning charged particle: mu = g * (q / (2m)) * S, using the gyromagnetic ratio and spin quantum number.
kg
Magnetic Moment
0.0000000000000000000000160809 J/T
In Bohr Magnetons1.734043 mu_B
Magnetic Moment vs g-Factor
Spin Magnetic Moment
A charged particle with intrinsic spin has a magnetic moment proportional to its angular momentum.
Formula
mu = g * (e / 2m) * S
where S = hbar * sqrt(s(s+1)) is the spin angular momentum.
For an electron, the magnetic moment is about 1 Bohr magneton = 9.274 x 10^-24 J/T.
Example Calculation
Electron: g = 2.0023, s = 1/2, m = 9.109e-31 kg.
- 01S = hbar * sqrt(s(s+1)) = 1.0546e-34 * sqrt(0.75) = 9.133e-35 J s
- 02mu = g * (e/2m) * S
- 03e/2m = 1.602e-19 / (2 * 9.109e-31) = 8.794e10 C/kg
- 04mu = 2.0023 * 8.794e10 * 9.133e-35 = 1.608e-23 J/T
- 05In Bohr magnetons: 2.0023 * sqrt(0.75) = 1.734 mu_B
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