Integration in Curvilinear Coordinates to Determine Total Charge

Integration using curvilinear coordinates has been introduced to most students in a multivariable calculus course prior to entering into upper-division electricity and magnetism courses, however, some students may not carry those skills immediately into physics. By reintroducing curvilinear coordinates, with the physics convention for $\theta$ and $\phi$, in a physical context, students can determine the total charge of a line, surface, or volume which are prevalent in electrostatic problems and essential to certain techniques such as Gauss's law.

Additionally, this sequence is intended to expand student understanding of integration to include integrals as measurable experimentally. Integrals can be measured by the accumulation of small pieces or small changes in measurable quantities. By including an experimental activity of integration, students can begin to more fluently use different representations of integration which likely already include FIXME (symbolic manipulation, area under a curve, and …).

Activities