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In continuous systems such as electromagnetic fields, fluid dynamics and deformable bodies, a momentum density can be defined as momentum per volume (a volume-specific quantity). A continuum version of the conservation of momentum leads to equations such as the Navier–Stokes equations for fluids or the Cauchy momentum equation for deformable ...
The density of the linear momentum of the electromagnetic field is S/c 2 where S is the magnitude of the Poynting vector and c is the speed of light in free space. The radiation pressure exerted by an electromagnetic wave on the surface of a target is given by P r a d = S c . {\displaystyle P_{\mathrm {rad} }={\frac {\langle S\rangle }{\mathrm ...
This equation is equivalent to the following 3D conservation laws + + = + + = + = respectively describing the electromagnetic energy density = (+) and electromagnetic momentum density =, where is the electric current density, the electric charge density, and is the Lorentz force density.
By expressing the shear tensor in terms of viscosity and fluid velocity, and assuming constant density and viscosity, the Cauchy momentum equation will lead to the Navier–Stokes equations. By assuming inviscid flow, the Navier–Stokes equations can further simplify to the Euler equations. The divergence of the stress tensor can be written as
The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor physical quantity that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics. It is an attribute of matter, radiation, and non-gravitational force fields.
In quantum mechanics, the probability current (sometimes called probability flux) is a mathematical quantity describing the flow of probability.Specifically, if one thinks of probability as a heterogeneous fluid, then the probability current is the rate of flow of this fluid.
The density of states related to volume V and N countable energy levels is defined as: = = (()). Because the smallest allowed change of momentum for a particle in a box of dimension and length is () = (/), the volume-related density of states for continuous energy levels is obtained in the limit as ():= (()), Here, is the spatial dimension of the considered system and the wave vector.
The formula needed in this case to calculate m in (units of A⋅m 2) is: =, where: B r is the residual flux density, expressed in teslas. V is the volume of the magnet (in m 3). μ 0 is the permeability of vacuum (4π × 10 −7 H/m). [6]