Magnetic energy

Magnetic energy and electrostatic potential energy are related by Maxwell's equations. The potential energy of a magnet or magnetic moment in a magnetic field is defined as the mechanical work of the magnetic force (actually magnetic torque) on the re-alignment of the vector of the magnetic dipole moment and is equal to:

while the energy stored in an inductor (of inductance ) when a current flows through it is given by:

This second expression forms the basis for superconducting magnetic energy storage.

Energy is also stored in a magnetic field. The energy per unit volume in a region of space of 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 , 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.[1]

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:[1]

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.[2]


  1. Jackson, John David (1998). Classical Electrodynamics (3 ed.). New York: Wiley. pp. 212–onwards.
  2. "The Feynman Lectures on Physics, Volume II, Chapter 15: The vector potential".
  • Magnetic Energy, Richard Fitzpatrick Professor of Physics The University of Texas at Austin.

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