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# Total Charge

**Keywords:**Electricity and Magnetism, Charge, Volume Charge Density, Scalar Fields, Coordinate Systems, Curvilinear Coordinates, Multiple Integral, Differential Elements, Small Group Activity

### Highlights of the activity

- This small group activity is designed to help upper-division undergraduate students calculate the total charge of various shapes.
- Students use multivariable integration in various coordinate systems in order to find the total charge of a given object with a specific charge density.
- The compare and contrast wrap-up discussion focuses on relating different volume charge densities and how the limits of integration are related to the shape of the object.

### Reasons to spend class time on the activity

Middle division students typically have very little experience working with non-constant charge densities and need practice integrating over spherical and cylindrical volumes. In this activity, students use their knowledge of differential volume elements in spherical and cylindrical coordinate systems. This activity also allows students to practice integrating by substitution.