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Paramagnetism: Instructor's Guide

Main Ideas

  • Total differentials
  • Cyclic chain rule
  • Legendre transformations
    • Chain rule diagrams
    • Differential substitution

Students' Task

Estimated Time: 35 minutes

  • Students evaluate two given partial derivatives
  • Students must use a Legendre transformation for one of the given partial derivatives
  • Students may find it helpful to use a chain rule diagram

Prerequisite Knowledge

  • Familiarity with partial derivatives and their interpretations
  • Familiarity with total differentials
  • Familiarity with Legendre transformations
  • Familiarity with the cyclical chain rule


Activity: Introduction

Activity: Student Conversations

  • Students may recognize one of the equations as a hyperbolic tangent. Credit them for recognizing it.
  • Students may find the physical truth of the equations to be inspiring, so do not hesitate to state that the equations are valid physical relations.
  • Students may ask what magnetic susceptibility, $\chi_B$, is. Dr. Round provides an eloquent response of sufficient detail: “It's the thing that's defined to be that.”
  • Students may be confused as to how to apply the cyclic chain rule.

Activity: Wrap-up


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