Infinitesimal calculus MOC

Divergence

The divergence of a vector field, also called the flux density, is a scalar measure of a vector field’s tendency to move away (i.e. to diverge) from a given point. It is given by

where is the gradient operator (sometimes called ). Interpreting as a velocity field of a fluid, the divergence represents the rate at which an infinitesimal volume changes with time.

Properties

• If everywhere, then is an Incompressible vector field, meaning it has a vector potential.
• Conversely, given continuous second order derivatives exist for .

Practice problems

See Practice problems.

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