Divergence and Curl Examples
Example 1: Consider the vector field . Find the divergence of and determine if the field is a source or a sink.
Solution:
Given,
- Vector Field
For Divergence,
= 3y + 0 – 2x
So, the divergence of is ( 3y – 2x )
To determine if it’s a source or sink, we need additional information about the region and boundary conditions.
- If 0 " title="Rendered by QuickLaTeX.com" height="27" width="109" style="vertical-align: 31px;">in a region, it’s a source
- If , it’s a sink
Example 2: Given the vector field , calculate the curl of and interpret its meaning in terms of rotation and circulation.
Solution:
For Vector Field: ,
For Curl:
⇒
⇒
⇒
So, the curl of is
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
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