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.
Magnetic Moment
0.0000000000000000000000160809 J/T
Magnetic Moment vs g-Factor
Formula
## 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. - *g* = Lande g-factor (approximately 2 for electrons) - *e* = elementary charge - *m* = particle mass For an electron, the magnetic moment is about 1 Bohr magneton = 9.274 x 10^-24 J/T.
Esempio Risolto
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
Domande Frequenti
Why is the electron g-factor not exactly 2?
Quantum electrodynamics predicts a small anomalous correction from virtual particle interactions. The measured value is 2.00231930436256, one of the most precise predictions in physics.
What is a Bohr magneton?
It is the natural unit of magnetic moment for the electron: mu_B = e * hbar / (2 m_e) = 9.274 x 10^-24 J/T.
Do neutrons have a magnetic moment?
Yes, despite being electrically neutral. This reveals the neutron's internal structure of quarks carrying fractional charges.
Impara