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Consider a long, thin rod of mass and length .To calculate the average linear mass density, ¯, of this one dimensional object, we can simply divide the total mass, , by the total length, : ¯ = If we describe the rod as having a varying mass (one that varies as a function of position along the length of the rod, ), we can write: = Each infinitesimal unit of mass, , is equal to the product of ...
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 ...
In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. [1] The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point.
Abstractly, a density is a section of a certain line bundle, called the density bundle. An element of the density bundle at x is a function that assigns a volume for the parallelotope spanned by the n given tangent vectors at x .
A linear operator between topological vector spaces and is said to be densely defined if its domain is a dense subset of and if its range is contained within . See also Continuous linear extension . A topological space X {\displaystyle X} is hyperconnected if and only if every nonempty open set is dense in X . {\displaystyle X.}
where: is the rate of change of the energy density in the volume. ∇•S is the energy flow out of the volume, given by the divergence of the Poynting vector S. J•E is the rate at which the fields do work on charges in the volume (J is the current density corresponding to the motion of charge, E is the electric field, and • is the dot product).
The density matrix is a representation of a linear operator called the density operator. The density matrix is obtained from the density operator by a choice of an orthonormal basis in the underlying space. [2] In practice, the terms density matrix and density operator are often used interchangeably.
The density of Lorentz force (that is, the linear momentum transferred from the electromagnetic field to matter within a 4-volume element divided by that element — do not use the metric in this calculation) is a covariant vector density of weight +1.