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Magnetic energy

From Wikipedia, the free encyclopedia

The potential magnetic energy of a magnet or magnetic moment in a magnetic field is defined as the mechanical work of the magnetic force on the re-alignment of the vector of the magnetic dipole moment and is equal to: The mechanical work takes the form of a torque : which will act to "realign" the magnetic dipole with the magnetic field.[1]

In an electronic circuit the energy stored in an inductor (of inductance ) when a current flows through it is given by: This expression forms the basis for superconducting magnetic energy storage. It can be derived from a time average of the product of current and voltage across an inductor.

Energy is also stored in a magnetic field itself. The energy per unit volume in a region of free space with vacuum permeability containing magnetic field is: More generally, if we assume that the medium is paramagnetic or diamagnetic so that a linear constitutive equation exists that relates and the magnetization (for example where is the magnetic permeability of the material), then it can be shown that the magnetic field stores an energy of where the integral is evaluated over the entire region where the magnetic field exists.[2]

For a magnetostatic system of currents in free space, the stored energy can be found by imagining the process of linearly turning on the currents and their generated magnetic field, arriving at a total energy of:[2] where is the current density field and is the magnetic vector potential. This is analogous to the electrostatic energy expression ; note that neither of these static expressions apply in the case of time-varying charge or current distributions.[3]

References

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  1. ^ Griffiths, David J. (2023). Introduction to electrodynamics (Fifth ed.). New York: Cambridge University Press. ISBN 978-1-009-39773-5.
  2. ^ a b Jackson, John David (1998). Classical Electrodynamics (3 ed.). New York: Wiley. pp. 212–onwards.
  3. ^ "The Feynman Lectures on Physics, Volume II, Chapter 15: The vector potential".
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  • Magnetic Energy, Richard Fitzpatrick Professor of Physics The University of Texas at Austin.