# 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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