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17: Magnetic Dipole Moment

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    • 17.1: Introduction to Magnetic Dipole Moments
      A number of different units for expressing magnetic dipole moment (hereafter simply “magnetic moment”) are commonly seen in the literature. It can be almost an impossibility, for example, to write down a list of the magnetic moments of the planets in order of increasing magnetic moment if one refers to the diverse literature in which the moments of each of the nine planets are quoted in different units. This chapter explores some of these aspects of magnetic moment.
    • 17.2: The SI Definition of Magnetic Moment
      If a magnet is placed in an external magnetic field B , it will experience a torque. The magnitude of the torque depends on the orientation of the magnet with respect to the magnetic field. There are two oppositely-directed orientations in which the magnet will experience the greatest torque, and the magnitude of the magnetic moment is defined as the maximum torque experienced by the magnet when placed in unit external magnetic field.
    • 17.3: The Magnetic Field on the Equator of a Magnet
      The magnetic field at a point at a distance r on the equator of a magnet may be expressed as a series of terms of successively higher powers of 1/r.
    • 17.4: CGS Magnetic Moment, and Lip Service to SI
      This page focuses on Equation 17.3.1, detailing the magnetic field on a magnet’s equator applicable in various unit systems. It warns against the use of numerical values that may misrepresent magnetic moments, especially in CGS EMU and when converting to SI units, potentially leading to confusion. The text emphasizes the distinction between different definitions and physical meanings of magnetic moments across contexts, urging careful representation to avoid misunderstandings.
    • 17.5: Possible Alternative Definitions of Magnetic Moment
      This page examines the different definitions of magnetic moment, influenced by the use of magnetic fields \(H\) or \(B\) and variations like the factor \(4\pi\). It presents six definitions, highlighting their distinct implications and the confusion over non-SI standards. A comparative table illustrates the differences in dimensions, units, and conversion factors between CGS and SI systems, demonstrating the practical impact of these definitions on scientific communication.
    • 17.6: Thirteen Questions
      This page covers the concept of magnetic moment, explaining its multiple definitions and their implications for understanding torque and magnetic fields. It highlights the importance of clarity in these definitions due to differing unit systems in literature.
    • 17.7: Additional Remarks
      This page explores the concept of magnetic moment, detailing its units (erg, joule) and their relationship to torque. It discusses the difficulties in defining magnetic moments, particularly through the potential energy expression \(-\boldsymbol{p.B}\), and addresses the use of nuclear magnetons in atomic measurements. Additionally, it provides examples of magnetic moments for Mercury and Uranus, highlighting the confusion stemming from differing conventions.
    • 17.8: Conclusion
      This page discusses the complexities of torque on a magnet in a magnetic field, noting confusion from differing interpretations of magnetic moment in literature. It stresses the need to follow the standard SI definition and units to prevent misunderstandings. Sections 17.2 and 17.3 encapsulate key points, illustrating that despite the concept appearing straightforward, terminological discrepancies lead to considerable confusion.

    Thumbnail: Magnetic fields can be visualized with iron filings, that align along the magnetic field direction. Here the magnetic field of a homogeneously magnetized cylindrical bar magnet was accurately computed, and the field is shown with simulated randomly placed iron filings. The density of filings is also proportional to the field strength. The field is strongest around the magnetic poles. (CC BY-SA 4.0; Geek3 via Wikipedia)

    This page titled 17: Magnetic Dipole Moment is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.