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The total energy in the space occupied by the system includes a component arising from the energy of a magnetic field in a vacuum. This component equals U v a c u u m = B e 2 V 2 μ 0 {\displaystyle U_{vacuum}={\frac {B_{e}^{2}V}{2\mu _{0}}}} , where μ 0 {\displaystyle \mu _{0}} is the permeability of free space , and isn't included as a part ...
In physics and mathematics, and especially differential geometry and gauge theory, the Yang–Mills equations are a system of partial differential equations for a connection on a vector bundle or principal bundle. They arise in physics as the Euler–Lagrange equations of the Yang–Mills action functional. They have also found significant use ...
With the appropriate choice of the imaginary current densities, the fields inside the surface or outside the surface can be deduced from the imaginary currents. [4] In a radiation problem with given current density sources, electric current density J 1 {\displaystyle J_{1}} and magnetic current density M 1 {\displaystyle M_{1}} , the tangential ...
where is the total angular momentum quantum number, and is the g-factor (such that = is the magnetic moment). For a two-level system with magnetic moment , the formula reduces to =, as above, while the corresponding expressions in Gaussian units are = (+), =.
In theoretical physics, the ' t Hooft–Polyakov monopole is a topological soliton similar to the Dirac monopole but without the Dirac string. It arises in the case of a Yang–Mills theory with a gauge group, coupled to a Higgs field which spontaneously breaks it down to a smaller group via the Higgs mechanism.
Magnetic current density, which has the unit V/m 2 (volt per square meter), is usually represented by the symbols and . [a] The superscripts indicate total and impressed magnetic current density. [1] The impressed currents are the energy sources. In many useful cases, a distribution of electric charge can be mathematically replaced by an ...
In this experiment, a static magnetic field runs through a long magnetic wire (e.g., an iron wire magnetized longitudinally). Outside of this wire the magnetic induction is zero, in contrast to the vector potential, which essentially depends on the magnetic flux through the cross-section of the wire and does not vanish outside.
Breakdown of ideal MHD (in the form of magnetic reconnection) is known to be the likely cause of solar flares. The magnetic field in a solar active region over a sunspot can store energy that is released suddenly as a burst of motion, X-rays, and radiation when the main current sheet collapses, reconnecting the field. [31] [32]