Schermerhorn Thompson on determining differential area elements

Student determination of differential area elements in upper-division physics

Benjamin P. Schermerhorn and John R. Thompson

Physics Education Research Conference Proceedings 2017

Given the significance of understanding differential area vectors in multivariable coordinate systems to the learning of electricity and magnetism (E&M), students in junior-level E&M were interviewed about E&M tasks involving integration over areas. In one task, students set up an integral for the magnetic flux through a square loop. A second task asked students to set up an integral to solve for the electric field from a circular sheet of charge. Analysis identified several treatments of the differential area: (1) a product of differential lengths, (2) a sum of differential lengths, (3) a product of a constant length with differential length in one direction, (4) a derivative of the expression for a given area, and (5) the full area.

Physics Education Research Conference 2017
Part of the PER Conference series
Cincinnati, OH: July 26-27, 2017
Pages 356-359

DOI: 10.1119/perc.2017.pr.084