# solenoidal field

A solenoidal vector field is one that satisfies

 $\nabla\cdot\mathbf{B}=0$

at every point where the vector field $\mathbf{B}$ is defined. Here $\nabla\cdot\mathbf{B}$ is the divergence.

This condition actually implies that there exists a vector $\mathbf{A}$, such that

 $\mathbf{B}=\nabla\times\mathbf{A}.$

For a function $f$ satisfying Laplace’s equation

 $\nabla^{2}f=0,$

it follows that $\nabla f$ is solenoidal.

Title solenoidal field SolenoidalField 2013-03-22 13:09:02 2013-03-22 13:09:02 giri (919) giri (919) 9 giri (919) Definition msc 26B12 solenoidal SourcesAndSinksOfVectorField