Divergence
Definition
How much a vector field spreads out from a point — positive where field lines are born (like charge), negative where they die.
Symbol: ·
Technical definition
∇·F = ∂F_x/∂x + ∂F_y/∂y + ∂F_z/∂z. Gauss's law in differential form reads ∇·E = ρ/ε₀.
Example
The electric field has positive divergence at a positive charge — field lines spray outward from it.
Common confusion
Divergence is a scalar (one number per point), not a vector. It measures net outflow — a swirling field can have zero divergence if nothing flows in or out.