Divergence of Vector Field
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, denoted as F(x, y). In two dimensions, for a vector field F(x, y), the divergence is given by:
In three dimensions, for a vector field F(x, y, z) represented as , the divergence is given by:
Divergence helps understand how a vector field’s behavior changes concerning a point, providing valuable insights into the field’s sources and sinks.
Divergence and Curl
Divergence and Curl are important concepts of Mathematics applied to vector fields. Divergence describes how a field behaves concerning or moving away from a point, while curl measures the rotational aspect of the field around a specific point. Divergence operators give scalar results whereas Curl operators give vector results.
In this article, we will learn about the divergence definition, curl definition, divergence of the vector field, curl of a vector field, and others in detail.
Table of Content
- What is Divergence?
- What is Curl?
- Divergence of Vector Field
- Curl of a Vector Field
- Divergence of Curl
- Equations of Divergence and Curl