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Charge density and delta functions -- SLAC Lightening Strike

Keywords: delta function, gauss, charge, divergence, E & M, Charge/Current Densities, Small Group


Highlights of the activity

Students start with basic delta function properties, then sketch a charge density described by a delta function. Next, they describe the charge density of a charged tube (SLAC) using a delta function. They check this answer in various ways. Then, symmetry is used to figure out which way the E-field points before using Gauss’s Law to calculate it. As a challenge problem, they figure out where in space there is a divergence.

Reasons to spend class time on the activity

Students often have difficulty understanding the dirac delta function as a representation of charge density. This is a subtle idea, using a foreign mathematical object (the dirac delta function) with pathological behavior. This tutorial really helped many students, who were struggling with this mathematical concept and relating it to the physical world.


Instructor's Guide


Authors: Darren Tarshis, Dr. Stephanie Chasteen, Dr. Steven Pollock all of the University of Colorado at Boulder
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