A vector field F satisfying the equation div F = 0 in domain D is called:
A) irrotational in D
B) a scalar potential
C) solenoidal in D
D) conservative in D
E) a vector potential

Question

Quizplus · Accepted Answer

A vector field $ \mathbf{F} $ satisfying $ \nabla \cdot \mathbf{F} = 0 $ is called solenoidal. This condition means that the divergence of $ \mathbf{F} $ is zero everywhere in the domain $ D $, indicating that there is no net "source" or "sink" at any point within $ D $. This property is characteristic of fields that are solenoidal, such as incompressible fluid flows or magnetic fields.

A Vector Field F Satisfying the Equation Div F =