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On the determination of divergence and curl from graphical representations.

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Bibliographic Details
Title: On the determination of divergence and curl from graphical representations.
Authors: Poljak, Nikola1 (AUTHOR) npoljak.phy@pmf.hr, Dulčić, Antonije1 (AUTHOR), Milin, Matko1 (AUTHOR), Požek, Miroslav1 (AUTHOR)
Source: European Journal of Physics. Jul2025, Vol. 46 Issue 4, p1-16. 16p.
Subjects: Vector calculus, Vectors (Calculus), Fluid dynamics, Electromagnetism, Intuition
Abstract: The divergence and curl operators are fundamental mathematical tools introduced in university-level electromagnetism courses. Although students generally understand the operational use of these concepts, developing a clear physical intuition of what divergence and curl are can be challenging. This difficulty often arises due to the superficial or confusing treatment found in many standard textbooks. The goal of this article is to provide a clear demonstration, based on examples, that two-dimensional visualizations can be misleading when used to interpret these operators. A combination of graphical and analytical (symbolic) representations was found to be essential for developing an accurate physical intuition about divergence and curl. A deeper comprehension of these operators not only improves proficiency in electromagnetism, but also benefits a range of other fields, from fluid dynamics to meteorology and to technical applications. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:The divergence and curl operators are fundamental mathematical tools introduced in university-level electromagnetism courses. Although students generally understand the operational use of these concepts, developing a clear physical intuition of what divergence and curl are can be challenging. This difficulty often arises due to the superficial or confusing treatment found in many standard textbooks. The goal of this article is to provide a clear demonstration, based on examples, that two-dimensional visualizations can be misleading when used to interpret these operators. A combination of graphical and analytical (symbolic) representations was found to be essential for developing an accurate physical intuition about divergence and curl. A deeper comprehension of these operators not only improves proficiency in electromagnetism, but also benefits a range of other fields, from fluid dynamics to meteorology and to technical applications. [ABSTRACT FROM AUTHOR]
ISSN:01430807
DOI:10.1088/1361-6404/addc1e