vector calculus a solenoidal vector field (also known as an incompressible vector field, a divergence-free vector field, or a transverse vector field)...

as the sum of a conservative vector field and a solenoidal field. A line integral of a vector field v {\displaystyle \mathbf {v} } is said to be path-independent...

be a solenoidal vector field. Let v : R 3 → R 3 {\displaystyle \mathbf {v} :\mathbb {R} ^{3}\to \mathbb {R} ^{3}} be a solenoidal vector field which...

calculus identities Vector algebra relations Directional derivative Conservative vector field Solenoidal vector field Laplacian vector field Helmholtz decomposition...

vector field, a vector field on a Riemannian manifold associated with a symmetry Solenoidal vector field, a vector field with zero divergence Vector potential...

It states that the magnetic field B has divergence equal to zero, in other words, that it is a solenoidal vector field. It is equivalent to the statement...

of the B-field produced this way is that magnetic B-field lines neither start nor end (mathematically, B is a solenoidal vector field); a field line may...

vectors in other words, ∇ × F = λ F {\displaystyle \nabla \times \mathbf {F} =\lambda \mathbf {F} } . If F {\displaystyle \mathbf {F} } is solenoidal...

and a solenoidal (divergence-free) vector field. In physics, often only the decomposition of sufficiently smooth, rapidly decaying vector fields in three...

solenoidal vector field (one with zero divergence) to S will result in another field that satisfies this required property of a Poynting vector field...

coordinates analysis of solenoidal vector fields, for example, magnetic fields and incompressible fluids. For a three-dimensional vector field F with zero divergence...

{A}}={\vec {B}}} ( A → {\displaystyle {\vec {A}}} is a vector potential for the solenoidal vector field B → {\displaystyle {\vec {B}}} ). Note that { d F =...

outside the sources. In a solenoidal vector field (i.e., a vector field where the divergence is zero everywhere), the field lines neither begin nor end;...

\mathbf {u} =0.} That is, if u {\displaystyle \mathbf {u} } is a solenoidal vector field. A flow is irrotational if the curl of u {\displaystyle \mathbf...

magnetic field is a solenoidal vector field. The Maxwell–Faraday version of Faraday's law of induction describes how a time-varying magnetic field corresponds...

magnetic fields are different facets of the same electromagnetic field, and in moving from one inertial frame to another, the solenoidal vector field portion...

(divergence) vanishes, and is called an incompressible flow (sometimes solenoidal vector field). The term incompressible is used because a non-zero divergence...

Scalar field Solenoidal vector field Stokes' theorem Submersion Surface integral Symmetry of second derivatives Taylor's theorem Total derivative Vector field...

constant c {\displaystyle \mathbf {c} } or any divergence free (solenoidal) vector field, e.g. Incompressible flows without sources or sinks such as phase...

an incompressible fluid the flow velocity field is a solenoidal vector field or a divergence-free vector field. Note that this relationship can be expanded...

the volume form is preserved under the flow of a solenoidal vector field. Thus solenoidal vector fields are precisely those that have volume-preserving...

vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source...

aU} The Stokes solution dissipates less energy than any other solenoidal vector field with the same boundary velocities: this is known as the Helmholtz...

Compressibility or Incompressible flow a property of a vector field, see Solenoidal vector field a topological property, see Incompressible surface a proof...

system; also called a starter relay Transmission solenoid Solenoidal vector field, a vector field in mathematics characterized as having zero divergence...

}}\rho \times {\vec {\nabla }}p} This vector, sometimes called the solenoidal vector, is of interest both in compressible fluids and in incompressible...

velocity field) into the equivalent role of the magnetic induction vector B in electromagnetism. In electromagnetism the B lines form solenoidal rings around...

incompressible. An incompressible flow is described by a solenoidal flow velocity field. But a solenoidal field, besides having a zero divergence, also has the...

thermal energy Solar wind Solarization (physics) Solarsoft Solenoid Solenoidal vector field Solid Solid-state ionics Solid-state laser Solid-state nuclear...

model generally represent the magnetic field by the solenoidal field B, analogous to the electrostatic field D. A generalization of the above current...