Orders of magnitude (magnetic moment): Difference between revisions

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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 ( $m {\displaystyle \mathbf {m} } <img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58d48fbdcdf404353d3d53cdc2b5968c35fa5125" aria-hidden="true" alt="{\displaystyle \mathbf {m} }" width="958.5" height="721.6">$ ) and the distance from its centre ( $r {\displaystyle r} <img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" aria-hidden="true" alt="{\displaystyle r}" width="451.5" height="721.6">$ ) it is possible to calculate the magnetic flux density experienced ( $B {\displaystyle \mathbf {B} } <img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cafb0ef39b0f5ffa23c170aa7f7b4e718327c4d1" aria-hidden="true" alt="{\displaystyle \mathbf {B} }" width="818.5" height="936.9">$ ) using the following approximation:

B ≈ μ 0 m 2 π r 3 , {\displaystyle \mathbf {B} \approx \mu _{0}{\frac {\mathbf {m} }{2\pi r^{3}}},} <img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52af3708229c24d372eccb389e17fef7b27d1903" aria-hidden="true" alt="{\displaystyle \mathbf {B} \approx \mu _{0}{\frac {\mathbf {m} }{2\pi r^{3}}},}" width="5827.9" height="2156.8">

where $μ 0 {\displaystyle \mu _{0}} <img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe2fd9b8decb38a3cd158e7b6c0c6e2d987fefcc" aria-hidden="true" alt="{\displaystyle \mu _{0}}" width="1057.4" height="936.9">$ is the vacuum permeability constant.

^ That is, $M P = l P 2 q P t P − 1 = 4 π G ε 0 ℏ 2 {\displaystyle \textstyle {\mathcal {M}}_{\text{P}}={l_{\text{P}}^{2}q_{\text{P}}}{t_{\text{P}}}^{-1}={\sqrt {4\pi G\varepsilon _{0}\hbar ^{2}}}} <img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdb8aeb9769afee85d5aee2b56c986c3287826c4" aria-hidden="true" alt="{\displaystyle \textstyle {\mathcal {M}}_{\text{P}}={l_{\text{P}}^{2}q_{\text{P}}}{t_{\text{P}}}^{-1}={\sqrt {4\pi G\varepsilon _{0}\hbar ^{2}}}}" width="13112.5" height="1510.9">$
^ 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): $μ i i D = 3 e G F m i 8 π 2 2 ≈ 3.2 × 10 − 19 m i 1 e V μ B {\displaystyle \mu _{ii}^{D}={\frac {3eG_{\text{F}}m_{i}}{8\pi ^{2}{\sqrt {2}}}}\approx 3.2\times 10^{-19}{\frac {m_{i}}{1\,eV}}\mu _{\text{B}}} <img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60c6ef4e3b86015ef58b654cf98b1df0905256dd" aria-hidden="true" alt="{\displaystyle \mu _{ii}^{D}={\frac {3eG_{\text{F}}m_{i}}{8\pi ^{2}{\sqrt {2}}}}\approx 3.2\times 10^{-19}{\frac {m_{i}}{1\,eV}}\mu _{\text{B}}}" width="16185.2" height="2730.8">$ , where $m i {\displaystyle m_{i}} <img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95ec8e804f69706d3f5ad235f4f983220c8df7c2" aria-hidden="true" alt="{\displaystyle m_{i}}" width="1222.8" height="865.1">$ is one of the possible neutrino masses, $G F {\displaystyle G_{\text{F}}} <img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/463ea1548afad99674dbb1436b7d611525bb1cb2" aria-hidden="true" alt="{\displaystyle G_{\text{F}}}" width="1348.6" height="1080.4">$ is Fermi’s constant and $μ B {\displaystyle \mu _{\text{B}}} <img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/094f7f8ca6e59db0ea0a055e864f1b9446c010b6" aria-hidden="true" alt="{\displaystyle \mu _{\text{B}}}" width="1204.5" height="936.9">$ is Bohr magneton.
^ 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.
^ Smite, Mara; Birjukovs, Mihails; Zvejnieks, Peteris; Drikis, Ivars; Kitenbergs, Guntars; Cebers, Andrejs (2025-01-16). “Explicit and fully automatic analysis of magnetotactic bacteria motion reveals the magnitude and length scaling of magnetic moments”. p. 17. arXiv:2501.09869 [abs].
^ ^a ^b 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.
^ 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
^ 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).
^ 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.
^ ^a ^b ^c “What is the MAGNETIC MOMENT?”. Adams Magnetic. 6 August 2021. Retrieved 2024-07-24.
^ 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.
^ ^a ^b Stanford Magnets (2024-06-03). “Magnetization Features: Magnetic Moment, Dipole, and Models”. Retrieved 2024-08-12.
^ ^a ^b This is a consequence of the definition of the magnetic constant.
^ ^a ^b ^c ^d ^e ^f 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].
^ “Earth’s Magnetic Field”. Harvard University. Retrieved 2024-07-24.
^ 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.
^ 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.

[1] That is, $M P = l P 2 q P t P − 1 = 4 π G ε 0 ℏ 2 {\displaystyle \textstyle {\mathcal {M}}_{\text{P}}={l_{\text{P}}^{2}q_{\text{P}}}{t_{\text{P}}}^{-1}={\sqrt {4\pi G\varepsilon _{0}\hbar ^{2}}}} <img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdb8aeb9769afee85d5aee2b56c986c3287826c4" aria-hidden="true" alt="{\displaystyle \textstyle {\mathcal {M}}_{\text{P}}={l_{\text{P}}^{2}q_{\text{P}}}{t_{\text{P}}}^{-1}={\sqrt {4\pi G\varepsilon _{0}\hbar ^{2}}}}" width="13112.5" height="1510.9">$

[studenikin-2016-2] 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): $μ i i D = 3 e G F m i 8 π 2 2 ≈ 3.2 × 10 − 19 m i 1 e V μ B {\displaystyle \mu _{ii}^{D}={\frac {3eG_{\text{F}}m_{i}}{8\pi ^{2}{\sqrt {2}}}}\approx 3.2\times 10^{-19}{\frac {m_{i}}{1\,eV}}\mu _{\text{B}}} <img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60c6ef4e3b86015ef58b654cf98b1df0905256dd" aria-hidden="true" alt="{\displaystyle \mu _{ii}^{D}={\frac {3eG_{\text{F}}m_{i}}{8\pi ^{2}{\sqrt {2}}}}\approx 3.2\times 10^{-19}{\frac {m_{i}}{1\,eV}}\mu _{\text{B}}}" width="16185.2" height="2730.8">$ , where $m i {\displaystyle m_{i}} <img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95ec8e804f69706d3f5ad235f4f983220c8df7c2" aria-hidden="true" alt="{\displaystyle m_{i}}" width="1222.8" height="865.1">$ is one of the possible neutrino masses, $G F {\displaystyle G_{\text{F}}} <img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/463ea1548afad99674dbb1436b7d611525bb1cb2" aria-hidden="true" alt="{\displaystyle G_{\text{F}}}" width="1348.6" height="1080.4">$ is Fermi’s constant and $μ B {\displaystyle \mu _{\text{B}}} <img decoding="async" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/094f7f8ca6e59db0ea0a055e864f1b9446c010b6" aria-hidden="true" alt="{\displaystyle \mu _{\text{B}}}" width="1204.5" height="936.9">$ 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] Smite, Mara; Birjukovs, Mihails; Zvejnieks, Peteris; Drikis, Ivars; Kitenbergs, Guntars; Cebers, Andrejs (2025-01-16). “Explicit and fully automatic analysis of magnetotactic bacteria motion reveals the magnitude and length scaling of magnetic moments”. p. 17. arXiv:2501.09869 [abs].

[gilder-et-al-5] 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.

[6] 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

[7] 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).

[8] 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.

[adamsmagnetic-9] “What is the MAGNETIC MOMENT?”. Adams Magnetic. 6 August 2021. Retrieved 2024-07-24.

[10] 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.

[neodymium-1cm-cube-11] Stanford Magnets (2024-06-03). “Magnetization Features: Magnetic Moment, Dipole, and Models”. Retrieved 2024-08-12.

[consequences-of-vacuum-permeability-12] This is a consequence of the definition of the magnetic constant.

[durand-manterola-13] ^ ^a ^b ^c ^d ^e ^f 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].

[14] “Earth’s Magnetic Field”. Harvard University. Retrieved 2024-07-24.

[15] 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.

[16] 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.

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+| rowspan=”2″ | Magnetic moment of [[magnetotactic bacteria]]
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Latest revision as of 02:59, 6 November 2025

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