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22. Inductance and Magnetic Energy

OCW Scholar

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Learning Objectives

  • To become familiar with the phenomena of self-inductance and how to calculate it for a given configuration of wires.
  • To comprehend the reason that energy is stored in inductors.
  • To relate the energy stored in inductors to the energy density of the magnetic field.
  • To comprehend how eddy current braking arises and how it relates to Faraday's Law.
  • To become familiar with the properties of transformers.

Preparation

Course Notes

Read through the course notes before watching the video.  The course note files may also contain links to associated animations or interactive simulations.

Read sections 11.1 though 11.4:
Inductance and Magnetic Energy (PDF - 1MB)

Lecture Video

Video Excerpts

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Learning Activities

Guided Activities

Read through the class slides. They explain all of the concepts from the module.

Slides (PDF - 1.7MB)

Self-Assessment

Once you have reviewed all the materials, try the Challenge Problems.

Challenge Problems

Challenge Problems (PDF)

Solutions (PDF)

Problem Solving Help

Watch the Problem Solving Help videos for insights on how to approach and solve problems related to the concepts in this module.

Problem 1: Pressure Due to a Magnetic Field in a Solenoid

A large solenoid with a radius of 0.5 meters and length of 2.5 meters has a magnetic field strength of 0.5 Tesla. How much energy is stored in this solenoid? How much current flows in a ring of height 1 centimeter along the length of this solenoid? How much force does this ring feel? What is the pressure on the ring? How does this pressure relate to the magnetic energy density in the solenoid?

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Problem 2: The Inductance of Two Co-axial Cables

Two co-axial cables have the same axis. They each have N windings and the same length l, but one has a radius a and the other has radius b. They are in series, so that they both carry the same current, but the windings are such that the magnetic field in one opposes the magnetic field of the other. What is the magnetic field everywhere? What is the self-inductance of this combination?

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Related Visualizations

The visualizations linked below are related to the concepts covered in this module.

 

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