In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the rate that the vector field alters the volume in an infinitesimal …

Dec 11, 2025 · In this section, we examine two important operations on a vector field: divergence and curl. They are important to the field of calculus for several reasons, including the use of …

Oct 25, 2025 · The divergence of a vector field is a scalar field, denoted as "div." To calculate the divergence, you take the scalar product of the vector operator (∇) applied to the vector field, …

Roughly speaking, divergence measures the tendency of the fluid to collect or disperse at a point, and curl measures the tendency of the fluid to swirl around the point. Divergence is a scalar, …

A magnetic field is a vector field that models the influence of electric currents and magnetic materials. Physicists use divergence in Gauss’s law for magnetism, which states that if B is a …

Dec 22, 2025 · A formula for the divergence of a vector field can immediately be written down in Cartesian coordinates by constructing a hypothetical infinitesimal cubical box oriented along …

Divergence (div) is “flux density”—the amount of flux entering or leaving a point. Think of it as the rate of flux expansion (positive divergence) or flux contraction (negative divergence).

Explore Divergence and Curl of a Vector Field, their physical meaning, formulas in various coordinate systems, solved examples, and practice questions.

Nov 16, 2022 · In this section we will introduce the concepts of the curl and the divergence of a vector field. We will also give two vector forms of Green’s Theorem and show how the curl can …

So now that we have an intuition for what divergence is trying to represent, let's start actually drilling in on a formula. The first thing I want to do is just limit our perspective to functions that …