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# Electric Field Due to a Ring of Charge

**Keywords:**Small Group Activity, Compare and Contrast, Computer Visualization, Mathematica, Coulomb's Law, Electric Field, Charge, Ring, Symmetry, Integral, Power Series, Superposition

### Highlights of the activity

- This small group activity is designed to help students wrestle with the concepts of charge density and electric field, as well as provide practice using power series approximations.
- Students are asked to create an integral expression for the electric field everywhere in space caused by a ring with total charge Q and radius R and to develop the power series expansion for the electric field near the center or far from the ring.
- The wrap-up discussion focuses on how to create an appropriate expression for an electric field.

### Reasons to spend class time on the activity

Two key concepts are introduced through this activity, one is gradient and the other is curvilinear vectors in the integrand.

Most students have a background that leads them to think of fields in terms of forces. Starting with electric potentials and using gradients to understand electric fields helps students build a much richer and deeper understanding. In addition developing the idea of fields from potentials “levels the playing field” because students have vastly different prior knowledge of the relationship between fields and forces, whereas nearly all students are novices at making the connection between potentials and fields. In this way the class can build a common understanding of fields without some students being bored and others being overwhelmed.