Student handout: Vector Surface and Volume Elements

Static Fields 2026
Students use \(d\boldsymbol{\vec{A} }= d\boldsymbol{\vec{r}}_1 \times d\boldsymbol{\vec{r}}_2\) and \(d\tau=(d\boldsymbol{\vec{r}}_1\times d\boldsymbol{\vec{r}}_2)\cdot d\boldsymbol{\vec{r}}_3\) to find differential surface and volume elements for cylinders and spheres.
What students learn Students use \(d\boldsymbol{\vec{A} }= d\boldsymbol{\vec{r}}_1 \times d\boldsymbol{\vec{r}}_2\) and \(d\tau=(d\boldsymbol{\vec{r}}_1\times d\boldsymbol{\vec{r}}_2)\cdot d\boldsymbol{\vec{r}}_3\) to find differential surface and volume elements for cylinders and spheres.
  1. Find the formulas for the differential area elements for:
    1. a plane (choose a easy one)
    2. a finite cylindrical shell (to the top/bottom and side separately),
    3. a spherical shell.

  2. Find the formulas for the differential volume elements for:

    1. a thick slab
    2. a cylinder
    3. a sphere

Editor
aran
Keywords
Learning Outcomes
Publication Status
Published
Publication Date
Nov. 5, 2026, 2:17 p.m.