Divergence: ∇·F = ∂P/∂x + ∂Q/∂y + ∂R/∂z. Measures net outflow per unit volume. ∇·F > 0: source. ∇·F < 0: sink. ∇·F = 0: incompressible. Divergence theorem: ∬F·dS = ∭∇·FdV.
How to Use
Select a vector field:
- F = (P,Q,R): Components
- Point: (x,y,z)
- Output: ∇·F at point
Physical Meaning
Positive divergence = fluid expanding outward (source). Negative = contracting inward (sink). Zero = volume-preserving (incompressible). Electric charge creates divergence in E field (Gauss's law).
Key Results
- ∇·(∇×F) = 0 always
- Gauss: ∬F·dS = ∭∇·FdV
- ∇·E = ρ/ε₀ (Maxwell)
Step-by-Step Instructions
- 1Select a vector field.
- 2Enter point (x,y,z).
- 3View divergence value.
- 4Check source/sink.
- 5Test incompressibility.