Orders of magnitude (magnetic moment)

This page lists examples of magnetic moments produced by various sources, grouped by orders of magnitude. The magnetic moment of an object is an intrinsic property and does not change with distance, and thus can be used to measure "how strong" a magnet is. For example, Earth possesses a large magnetic moment, but due to the radial distance, we experience only a tiny magnetic flux density on its surface.

Knowing the magnetic moment of an object (${\displaystyle \mathbf {m} }$) and the distance from its centre (${\displaystyle r}$) it is possible to calculate the magnetic flux density experienced (${\displaystyle \mathbf {B} }$) using the following approximation:

${\displaystyle \mathbf {B} \approx \mu _{0}{\frac {\mathbf {m} }{2\pi r^{3}}},}$

where ${\displaystyle \mu _{0}}$ is the vacuum permeability constant.

Examples

Magnetic dipole moments

Factor (m 2⋅A)	Value	Item
10−45	9.09×10−45 m2⋅A [1]	Unit of magnetic moment in Planck units
10−43	~1×10−43 m2⋅A [2]	Expected magnetic moment of a neutrino
10−27	4.3307346×10−27 m2⋅A	Magnetic moment of a deuterium nucleus
10−26	1.4106067×10−26 m2⋅A	Magnetic moment of a proton
10−24	9.284764×10−24 m2⋅A	Magnetic moment of a positron
	9.274...×10−24 m2⋅A	Bohr magneton
10−18	0.65–2.65 nm2⋅A (1 nm2⋅A = 10−18 m2⋅A) [3]	Magnetic moment of individual magnetite nanoparticles (20 nm diameter)
10−11	1.5×10−11 m2⋅A [4]	Magnetic moment of the human brain
	3.75×10−11 m2⋅A [4]
10−5	7.99×10−5 m2⋅A [5] [6]	NIST YIG (yttrium iron garnet) standard 1 mm sphere for calibrating magnetometers (SRM #2852)
10−4	8.6×10−4 m2⋅A [7]	Needle in a thumbnail-sized compass
10−3	7.909×10−3 m2⋅A [8]	Neodymium–iron–boron disc in a typical mobile phone
10−1	0.1 m2⋅A [9]	Magnetic field of a typical refrigerator magnet
	0.4824 m2⋅A [8]	Neodymium–iron–boron (strongest grade) disc the same size as a US penny
100	1.17 m2⋅A [10]	Neodymium–iron–boron N35 magnet with a volume of 1 cm3
	1.42 m2⋅A [10]	Neodymium–iron–boron N52 magnet with a volume of 1 cm3
103	5.937×103 m2⋅A [8]	A bowling ball made of neodymium–iron–boron (strongest grade)
106	5×106 m2⋅A [11]	A magnet that produces one tesla one metre away from its centre
1012	5×1012 m2⋅A [11]	A magnet that produces one tesla 100 m away from its centre
1019	4×1019 m2⋅A [12]	Magnetic moment of Mercury
1020	1.32×1020 m2⋅A [12]	Magnetic moment of Ganymede
1022	6.4×1022 m2⋅A [13]	Magnetic moment of Earth
1024	2.2×1024 m2⋅A [12]	Magnetic moment of Neptune
	3.9×1024 m2⋅A [12]	Magnetic moment of Uranus
1025	4.6×1025 m2⋅A [12]	Magnetic moment of Saturn
1027	1.55×1027 m2⋅A [12]	Magnetic moment of Jupiter
1028	1×1028 m2⋅A	Magnetic moment of a star, a white dwarf or a magnetar [14]
1029	1×1029 m2⋅A
1030	1×1030 m2⋅A [15]

References

1. That is, ${\displaystyle \textstyle {\mathcal {M}}_{\text{P}}={l_{\text{P}}^{2}q_{\text{P}}}{t_{\text{P}}}^{-1}={\sqrt {4\pi G\varepsilon _{0}\hbar ^{2}}}}$
2. Studenikin, Alexander (2016). "Status and perspectives of neutrino magnetic moments". J. Phys. Conf. Ser. 718 (62076). IOPscience. arXiv: 1603.00337 . Bibcode:2016JPhCS.718f2076A. doi:10.1088/1742-6596/718/6/062076 . Retrieved 2025-04-25. See in particular equation (5): ${\displaystyle \mu _{ii}^{D}={\frac {3eG_{\text{F}}m_{i}}{8\pi ^{2}{\sqrt {2}}}}\approx 3.2\times 10^{-19}{\frac {m_{i}}{1\,eV}}\mu _{\text{B}}}$, where ${\displaystyle m_{i}}$ is one of the possible neutrino masses, ${\displaystyle G_{\text{F}}}$ is Fermi's constant and ${\displaystyle \mu _{\text{B}}}$ is Bohr magneton.
3. Sievers, Sibylle; Braun, Kai-Felix; Eberbeck, Dietmar; Gustafsson, Stefan; Olsson, Eva; Schumacher, Hans Werner; Siegner, Uwe (2012-09-10). "Quantitative Measurement of the Magnetic Moment of Individual Magnetic Nanoparticles by Magnetic Force Microscopy". Small . 8 (17): 2675–2679. Bibcode:2012Small...8.2675S. doi:10.1002/smll.201200420. PMC   3561699 . PMID   22730177.
4. Gilder, Stuart A.; Wack, Michael; Kaub, Leon; Roud, Sophie C.; Petersen, Nikolai; Heinsen, Helmut; Hillenbrand, Peter; Milz, Stefan; Schmitz, Christoph (2018). "Distribution of magnetic remanence carriers in the human brain". Scientific Reports. 8 (11363): 11363. Bibcode:2018NatSR...811363G. doi:10.1038/s41598-018-29766-z. PMC   6063936 . PMID   30054530.
5. Erdevig, Hannah E.; Russek, Stephen E.; Carnicka, Slavka; Stupic, Karl F.; Keenan, Kathryn E. (May 2017). "Accuracy of magnetic resonance based susceptibility measurements". AIP Advances . 7 (5) 056718. Bibcode:2017AIPA....7e6718E. doi: 10.1063/1.4975700 . The SQUID magnetometer is calibrated with a NIST YIG (yttrium iron garnet) sphere standard reference material (SRM #2852) whose room temperature moment is (79.9 ± 0.3) × 10⁻⁶ A·m²
6. Handwerker, Carol A.; John, Rumble (2002-05-20). "Certificate of Analysis – Standard Reference Material 2853 – Magnetic Moment Standard - Yttrium Iron Garnet Sphere" (PDF). National Institute of Standards and Technology . Retrieved 2024-08-13. SRM 2853 consists of a yttrium iron garnet (YIG) sphere with a nominal diameter of 1 mm and a nominal mass 2.8 mg. The certified value for the specific magnetization, σ, at 298 K in an applied magnetic field of 398 kA/m (5000 Oe) is: σ = 27.6 A·m²/kg ± 0.1 A·m²/kg (27.6 emu/g ± 0.1 emu/g).
7. Cookson, Esther; Nelson, David; Michael, Anderson; McKinney, Daniel L.; Barsukov, Igor (2019). "Exploring Magnetic Resonance with a Compass". Phys. Teach. 57 (9): 633–635. arXiv: 1810.11141 . Bibcode:2019PhTea..57..633C. doi:10.1119/1.5135797 . Retrieved 2024-08-09. For a thumbnail-sized compass, we (empirically) estimate the magnetic moment to 0.86×10⁻³ A⋅m² and the moment of inertia to 1.03×10⁻¹¹ kg⋅m².
8. "What is the MAGNETIC MOMENT?". Adams Magnetic. 6 August 2021. Retrieved 2024-07-24.
9. Tal, Assaf (2021). "Imaging the Brain using MRI: From Physics to Applications – Lecture 3, Spin Dynamics" (PDF). Weizmann Institute Of Science. Retrieved 2024-08-09. A typical refrigerator magnet might have a macroscopic magnetic moment of about 0.1  J/T.
10. Stanford Magnets (2024-06-03). "Magnetization Features: Magnetic Moment, Dipole, and Models" . Retrieved 2024-08-12.
11. This is a consequence of the definition of the magnetic constant.
12. Durand-Manterola, Hector Javier (2010-07-26). "Dipolar Magnetic Moment of the Bodies of the Solar System and the Hot Jupiters". arXiv: 1007.4497 [astro-ph.EP].
13. "Earth's Magnetic Field". Harvard University. Retrieved 2024-07-24.
14. Magnetars have enormous magnetic flux densities on their surfaces due to the small radius, however the total magnetic field of the original star does not increase during the collapse, but actually decreases with time. Cf. Reisenegger, A. (2003). "Origin and Evolution of Neutron Star Magnetic Fields". arXiv: astro-ph/0307133 . Generally speaking, young neutron stars appear to have strong magnetic fields ~10¹¹⁻¹⁵ G ('classical' radio pulsars, 'magnetars', X-ray pulsars), whereas old neutron stars have weak fields ≲ 10⁹ G (ms pulsars, lowmass X-ray binaries). If these two groups have an evolutionary connection, their dipole moment must decay. Millisecond pulsars are believed to have been spun up to their fast rotation by accretion from a binary companion, a remnant of which is in most cases still present (e.g., Phinney & Kulkarni 1994). The reduction in the magnetic dipole moment may be a direct or indirect consequence of the accretion process, or just an effect of age.
15. Toropina, O. D.; Romanova, M. M.; Lovelace, R. V. E. (2006). "Spinning-down of moving magnetars in the propeller regime". Monthly Notices of the Royal Astronomical Society. 371 (2): 569–576. arXiv: astro-ph/0606254 . Bibcode:2006MNRAS.371..569T. doi: 10.1111/j.1365-2966.2006.10667.x .

See also

• Orders of magnitude (magnetic flux density)