Electromagnetic conic sections

Dray, Tevian; Manogue, Corinne A.

doi:doi:10.1119/1.1501115

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American Journal of Physics -- November 2002 -- Volume 70, Issue 11, pp. 1129

Electromagnetic conic sections

Tevian Dray¹ and Corinne A. Manogue²

¹Department of Mathematics, Oregon State University, Corvallis, Oregon 97331
²Department of Physics, Oregon State University, Corvallis, Oregon 97331

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Certain orthogonal coordinate systems naturally correspond to basis vectors which are both curl-free and divergence-free, and hence solve Maxwell’s equations. After first comparing several different traditional approaches to computing div, grad, and curl in curvilinear coordinates, we present a new approach, based on these “electromagnetic” basis vectors, which combines geometry and physics. Not only is our approach tied to a physical interpretation in terms of the electromagnetic field, it is also a useful way to remember the formulas themselves. We give several important examples of coordinate systems in which this approach is valid, in each case discussing the electromagnetic interpretation of the basis. We also give a general condition for when an electromagnetic interpretation is possible. © 2002 American Association of Physics Teachers.