A simplified approach to electromagnetism using geometric algebra

James M. Chappell; Azhar Iqbal; Derek Abbott

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arXiv · 1010.4947

A simplified approach to electromagnetism using geometric algebra

James M. Chappell·Azhar Iqbal·Derek Abbott

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Abstract

A new simplified approach for teaching electromagnetism is presented using the formalism of geometric algebra (GA) which does not require vector calculus or tensor index notation, thus producing a much more accessible presentation for students. The four-dimensional spacetime proposed is completely symmetrical between the space and time dimensions, thus fulfilling Minkowski's original vision. In order to improve student reception we also focus on forces and the conservation of energy and momentum, which take a very simple form in GA, so that students can easily build on established intuitions in using these laws developed from studying Newtonian mechanics. The potential formulation is also integrated into the presentation that allows an alternate solution path, as well as an introduction to the Lagrangian approach. Several problems are solved throughout the text to make the implementation clear. We extend previous treatment of this area, through including the potential formulation, the conservation of energy and momentum, the generalization for magnetic monopoles, as well as simplifying previously reported results through eliminating the need for the spacetime metric.

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James M. Chappell, Azhar Iqbal, Derek Abbott. 2010-11-10. A simplified approach to electromagnetism using geometric algebra. https://arxiv.org/abs/1010.4947

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