solenoidal field


A solenoidal vector field is one that satisfies

βˆ‡β‹…π=0

at every point where the vector field 𝐁 is defined. Here βˆ‡β‹…π is the divergence.

This condition actually implies that there exists a vector 𝐀, such that

𝐁=βˆ‡Γ—π€.

For a function f satisfying Laplace’s equation

βˆ‡2⁑f=0,

it follows that βˆ‡β‘f is solenoidal.

Title solenoidal field
Canonical name SolenoidalField
Date of creation 2013-03-22 13:09:02
Last modified on 2013-03-22 13:09:02
Owner giri (919)
Last modified by giri (919)
Numerical id 9
Author giri (919)
Entry type Definition
Classification msc 26B12
Synonym solenoidal
Related topic SourcesAndSinksOfVectorField