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...]] <math>\partial_\mu j^\mu=0</math>. The continuity equation represents a conservation law, hence the name. ...h>, large enough to have no net currents through its surface, leads to the conservation law ...

...[continuous symmetry]] leads to a fundamental [[Conservation law (physics)|conservation law]]. ...is generally means that the form of the law (e.g. the type of differential equations used to describe the law) is unchanged in transformations so that no additi ...

...translation symmetry is closely connected, via [[Noether's theorem]], to [[conservation of energy]].<ref name=Wilczek>{{cite book|last1=Wilczek|first1=Frank|title= ...tion it is said to be ''invariant''. Symmetries in nature lead directly to conservation laws, something which is precisely formulated by [[Noether's theorem]].<ref ...

== Conservation laws == {{Further|Conservation laws}} ...

The free [[Maxwell equations]] imply that ...ifferential conservation law for <math>Z^0</math>, Lipkin found other nine conservation laws, all unrelated to the [[stress–energy tensor]]. He collectively named ...

...solved using linear algebra by computer. Because of the compact system of equations, many [[circuit simulation]] programs (e.g., [[SPICE]]) use nodal analysis ...n simplify the analysis. For a circuit of ''N'' nodes the number of nodal equations is ''N''−1. ...

In special relativity, the statement of [[charge conservation]] is that the [[Lorentz invariant]] divergence of ''J'' is zero:<ref>J. D. == Maxwell's equations == ...

...]] [[gauge transformation]] of [[Quantum electrodynamics|QED]] implies the conservation of the [[electric charge]]. Likewise, if a theory possesses an internal chi ...role in [[hadron|hadronic physics]].) An important consequence of such non-conservation is the neutral [[pion]] [[Particle decay|decay]] and the [[chiral anomaly]] ...

...from one frame to another. However, this is not as general as [[Maxwell's equations in curved spacetime]] or non-rectilinear coordinate systems. ...in a vacuum, one could instead regard them as the formulation of Maxwell's equations in terms of ''total'' charge and current. ...

...apm.12133 Toward a General Solution of the Three-Wave Resonant Interaction Equations]'', Studies in Applied Mathematics, Volume '''137''', Issue 1. ...due to [[nonlinearity]]. The theory is based partly on the [[principle of conservation of energy]]. It requires that [[energy storage]] in the circuit is a [[stat ...

...scribed by the [[Navier–Stokes equations]]—a set of [[partial differential equations]] which are based on: * continuity ([[continuity equation#Fluid dynamics|conservation of mass]]), ...

...ll's equations#Conventional formulation in SI units|SI units for Maxwell's equations]] and the [[sign convention#Metric signature|particle physicist's sign conv ...e 4-current density 1-form, is the differential forms version of Maxwell's equations. ...

==Equations for fluids== ...efinition, mass flux is also equal to:<ref>Vectors, Tensors, and the basic Equations of Fluid Mechanics, R. Aris, Dover Publications, 1989, {{ISBN|0-486-66110-5 ...

Therefore, the [[energy conservation law]] is fulfilled by the model. ...</math> and <math>H_z</math> (i.e. a TE-mode distribution), then Maxwell's equations in [[Cartesian coordinates]] reduce to ...

...y a [[Spring (device)|spring]]. If the pendulums are identical, then their equations of motion are given by These equations represent the [[simple harmonic motion]] of the pendulum with an added coup ...

{{about|the conservation of electric charge|a general theoretical concept|charge (physics)}} In [[physics]], '''charge conservation''' is the principle that the total [[electric charge]] in an [[isolated sys ...

...plicated, this ordinary procedure can become impractically difficult, with equations spanning multiple lines. It is therefore convenient to collect many of thes ...th> and <math>\mathbf{B}</math>. Using [[vector calculus]] and [[Maxwell's equations]], symmetry is sought for in the terms containing <math>\mathbf{E}</math> a ...

...this, the various angular differences can be calculated in the power flow equations. If a slack bus is not specified, then a generator bus with maximum real po ...ince it will account for transmission line losses. In a load flow problem, conservation of energy results in the total generation equaling to the sum of the loads. ...

...page 11</ref><blockquote>The concept of co-energy can be applied to many [[Conservation law (physics)|conservative systems]] (inertial mechanical, electromagnetic, The last two expressions are general equations for energy and coenergy in magnetostatic system. ...

...ics]], two or more [[mass]]es always have a [[gravitational potential]]. [[Conservation of energy]] requires that this gravitational field energy is always negativ ...rticle then crosses the event horizon into the black hole, with the law of conservation of energy requiring that an equal amount of positive energy should escape. ...