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Maxwell's equations are used in physics to describe the relationship between electric and magnetic fields. Normally given as four differential equations they have a particularly compact form when the fields are expressed as a spacetime bivector from ⋀ 2 R 3,1. If the electric and magnetic fields in R 3 are E and B then the electromagnetic ...
conserved, bivector Angular velocity: ω: The angle incremented in a plane by a segment connecting an object and a reference point per unit time rad/s T −1: bivector Area: A: Extent of a surface m 2: L 2: extensive, bivector or scalar Centrifugal force: F c: Inertial force that appears to act on all objects when viewed in a rotating frame of ...
the bivector has two distinct principal null directions; in this case, the bivector is called non-null. Furthermore, for any non-null bivector, the two eigenvalues associated with the two distinct principal null directions have the same magnitude but opposite sign, λ = ±ν, so we have three subclasses of non-null bivectors: spacelike: ν = 0
The derivatives that appear in Maxwell's equations are vectors and electromagnetic fields are represented by the Faraday bivector F. This formulation is as general as that of differential forms for manifolds with a metric tensor, as then these are naturally identified with r -forms and there are corresponding operations.
A two-vector or bivector [1] is a tensor of type () and it is the dual of a two-form, meaning that it is a linear functional which maps two-forms to the real numbers (or more generally, to scalars). The tensor product of a pair of vectors is a two-vector. Then, any two-form can be expressed as a linear combination of tensor products of pairs of ...
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
A bivector is an element of the antisymmetric tensor product of a tangent space with itself. In geometric algebra , also, a bivector is a grade 2 element (a 2-vector) resulting from the wedge product of two vectors, and so it is geometrically an oriented area , in the same way a vector is an oriented line segment.
Symbol Meaning SI unit of measure magnetic vector potential: tesla meter (T⋅m) : area: square meter (m 2) : amplitude: meter: atomic mass number: unitless acceleration: meter per second squared (m/s 2)