Bibliographic Details
| Title: |
Integration between Physics and Mathematics: the relation between Green's functions and method of images as a worked example. |
| Authors: |
Cohen Pantoja, Glauco1 glauco.pantoja@ufopa.edu.br, de Sousa Elias, Walace2 |
| Source: |
Latin-American Journal of Physics Education. Dec2022, Vol. 16 Issue 4, p1-11. 11p. |
| Subject Terms: |
Green's functions, Electrostatics |
| Abstract (English): |
In the present work we discuss how to address the solution of electrostatic problems, in professional cycle of undergraduate course in science or engineering, using Green's functions and the Poisson's equation. For this, it is considered the structural role that mathematics, especially Green's function, has in physical thought presented in the method of images. By using this procedure and discussing the historical construction of Green's problem, it was possible to verify its relationship with the method of images as an interdisciplinary approach that is not developed in didactic physics textbooks. The possibility of analyzing Green's function as the result of two tasks, namely, the reduction of a continuous charge distribution to the one due to a point charge and the solution of the problem as the superposition of potentials due to sets of point charges continuously distributed represented by the integration of the Green's function over the electric charge density, is our account for teaching implication that shows, at the same time, epistemological ruptures and continuities to teaching-learning processes. [ABSTRACT FROM AUTHOR] |
| Abstract (Spanish): |
En el presente trabajo discutimos cómo abordar la solución de problemas electrostáticos, en ciclos profesionales de licenciatura en ciencias o ingeniería, utilizando las funciones de Green y la ecuación de Poisson. Para ello, se considera el papel estructural que tiene la matemática, en especial la función de Green, en el pensamiento físico presentado en el método de las imágenes. Al utilizar este procedimiento y discutir la construcción histórica del problema de Green, fue posible verificar su relación con el método de las imágenes como un enfoque interdisciplinario que no se desarrolla en los libros de texto de física didáctica. Se representa la posibilidad de analizar la función de Green como resultado de dos tareas, a saber, la reducción de una distribución de carga continua a la debida a una carga puntual y la solución del problema como la superposición de potenciales debido a conjuntos de cargas puntuales distribuidas de forma continua. por la integración de la función de Green sobre la densidad de carga eléctrica, es nuestra explicación de la implicación docente que muestra, al mismo tiempo, rupturas epistemológicas y continuidades en los procesos de enseñanza-aprendizaje. [ABSTRACT FROM AUTHOR] |
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| Database: |
Education Research Complete |
