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The term magnetic potential can be used for either of two quantities in classical electromagnetism: the ''magnetic vector potential'', A, (often simply called the ''vector potential'') and the ''magnetic scalar potential'', ψ. Both quantities can be used in certain circumstances to calculate the magnetic field. The more frequently used magnetic vector potential, A, is defined such that the curl of A is the magnetic field B. Together with the electric potential, the magnetic vector potential can be used to specify the electric field, E as well. Therefore, many equations of electromagnetism can be written either in terms of the E and B, ''or'' in terms of the magnetic vector potential and electric potential. In more advanced theories such as quantum mechanics, most equations use the potentials and not the E and B fields. The magnetic scalar potential ψ is sometimes used to specify the magnetic H-field in cases when there are no free currents, in a manner analogous to using the electric potential to determine the electric field in electrostatics. One important use of ψ is to determine the magnetic field due to permanent magnets when their magnetization is known. With some care the scalar potential can be extended to include free currents as well. == Magnetic vector potential == The magnetic vector potential A is a vector field defined along with the electric potential ''ϕ'' (a scalar field) by the equations: : where B is the magnetic field and E is the electric field. In magnetostatics where there is no time-varying charge distribution, only the first equation is needed. (In the context of electrodynamics, the terms "vector potential" and "scalar potential" are used for "magnetic vector potential" and "electric potential", respectively. In mathematics, vector potential and scalar potential have more general meanings.) Defining the electric and magnetic fields from potentials automatically satisfies two of Maxwell's equations: Gauss's law for magnetism and Faraday's Law. For example, if A is continuous and well-defined everywhere, then it is guaranteed not to result in magnetic monopoles. (In the mathematical theory of magnetic monopoles, A is allowed to be either undefined or multiple-valued in some places; see magnetic monopole for details). Starting with the above definitions: : : Alternatively, the existence of A and ''ϕ'' is guaranteed from these two laws using the Helmholtz's theorem. For example, since the magnetic field is divergence-free (Gauss's law for magnetism), i.e. ∇ • B = 0, A always exists that satisfies the above definition. The vector potential A is used when studying the Lagrangian in classical mechanics and in quantum mechanics (see Schrödinger equation for charged particles, Dirac equation, Aharonov–Bohm effect). In the SI system, the units of A are V·s·m−1 and are the same as that of momentum per unit charge. Although the magnetic field B is a pseudovector (also called axial vector), the vector potential A is a polar vector.〔(Tensors and pseudo-tensors, lecture notes by Richard Fitzpatrick )〕 This means that if the right-hand rule for cross products were replaced with a left-hand rule, but without changing any other equations or definitions, then B would switch signs, but A would not change. This is an example of a general theorem: The curl of a polar vector is a pseudovector, and vice versa.〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「magnetic potential」の詳細全文を読む スポンサード リンク
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