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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.
Magnetic potential energy is the form of energy related not only to the distance between magnetic materials, but also to the orientation, or alignment, of those materials within the field. For example, the needle of a compass has the lowest magnetic potential energy when it is aligned with the north and south poles of the Earth's magnetic field.
A magnetic moment in an externally produced magnetic field has a potential energy U: = In a case when the external magnetic field is non-uniform, there will be a force, proportional to the magnetic field gradient , acting on the magnetic moment itself.
The magnetic potential energy per unit volume ... One application of demagnetization is to eliminate unwanted magnetic fields. For example, magnetic fields can ...
The energy of a localized magnetic charge q m in a magnetic scalar potential is =, and of a magnetic charge density distribution ρ m in space =, where µ 0 is the vacuum permeability. This is analog to the energy Q = q V E {\displaystyle Q=qV_{E}} of an electric charge q in an electric potential V E {\displaystyle V_{E}} .
For example, the sum of translational and rotational kinetic and potential energy within a system is referred to as mechanical energy, whereas nuclear energy refers to the combined potentials within an atomic nucleus from either the nuclear force or the weak force, among other examples.
The magnetic vector potential, , is a vector field, and the electric potential, , is a scalar field such that: [5] = , =, where is the magnetic field and is the electric field. In magnetostatics where there is no time-varying current or charge distribution , only the first equation is needed.
In advanced classical mechanics it is often useful, and in quantum mechanics frequently essential, to express Maxwell's equations in a potential formulation involving the electric potential (also called scalar potential) φ, and the magnetic potential (a vector potential) A. For example, the analysis of radio antennas makes full use of Maxwell ...