21. Faraday's Law

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• Syllabus
• Electric Fields

  • 1. Introduction to Electric Fields
  • 2. Math Review, Fields
  • 3. Electric Fields and Discrete Charge Distributions
  • 4. Electric Fields and Continuous Charge Distributions
  • 5. Gauss's Law
• Electric Potential

  • 6. Discrete and Continuous Distributions of Charge
  • 7. Equipotential Lines and Electric Fields
  • 8. Gauss's Law and Configuration Energy
• Capacitors

  • 9. Conductors and Insulators, Conductors as Shields
  • 10. Capacitance and Capacitors, Energy Stored in Capacitors
  • 11. Capacitors and Dielectrics
• Circuits

  • 12. Current, Current Density, Resistance, and Ohm's Law
  • 13. Batteries and Circuit Elements
  • 14. DC Circuits
  • 15. DC Circuits with Capacitors
• Magnetic Fields and Forces

  • 16. Magnetic Field
  • 17. Magnetic Forces
  • 18. Magnetic Dipoles
• Creating Magnetic Fields

  • 19. Biot-Savart Law
  • 20. Ampere's Law
• Faraday's Law

  • 21. Faraday's Law
  • 22. Inductance and Magnetic Energy
  • 23. RL Circuits
• Oscillating Circuits

  • 24. Undriven RLC Circuits
  • 25. Driven RLC Circuits
• Maxwell's Equations

  • 26. The Displacement Current and Maxwell's Equations
  • 27. Poynting Vector and Energy Flow in a Capacitor
• Electromagnetic Waves

  • 28. Maxwell's Equations and Electromagnetic Waves
  • 29. Energy and Momentum in Electromagnetic Waves
  • 30. Generating EM Waves, Dipole Radiation and Polarization
• Nature of Light

  • 31. Interference
  • 32. Diffraction
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Learning Objectives

• To become familiar with the physical phenomena associated with Faraday's Law.
• To review the meaning of the flux of a field through an open surface.
• To comprehend the meaning of the statement that the induced emf is given by the negative of the time rate of change of the magnetic flux.
• To categorize the various ways we use to induce an emf.

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.

Faraday's Law of Induction (PDF)

Lecture Video

Video Excerpts

Learning Activities

Guided Activities

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

Slides (PDF - 1.4MB)

Self-Assessment

Do the Concept Questions first to make sure you understand the main concepts from this module. Then, when you are ready, try the Challenge Problems.

Concept Questions

Concept Questions (PDF)

Solutions (PDF - 1.2MB)

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: Induced Current due to a Time-Changing Magnetic Field

A uniform magnetic field is directed into the page, and is decreasing at a constant rate. A conducting ring of radius d and resistance R lies in the page. What is the magnitude and direction of the induced current in the loop? Pick a point a and b on opposite sides of the ring. What is the potential difference between these two points?

Problem 2: A Loop of Wire Moving in A Non-Uniform B Field

A square loop of side L has resistance R and moves at constant speed to the right in the plane of the page. It moves from a field free region into a region where the magnetic field is into the page and constant. This region of non-zero field is a square with sides of length 2L, and the magnetic field strength in this region is B. What is the external force required to move this loop at constant speed through this region of non-zero field? Sketch a graph of this force as a function of the position of the loop.

Problem 3: Magnetic Flux due to an Infinite Wire through a Rectangular Loop

A long straight wire is vertical and carries a current I which is vertical and increasing steadily at the constant rate of dI/dt. Consider a rectangular wire loop of resistance R, two of whose sides are parallel to the long straight wire, and whose plane contains the long straight wire. The distance from the long straight wire to the nearest parallel side of the loop is a, and the distance to the furtherest parallel side of the loop is b. The length of the wire loop parallel to the wire is l. What is the induced current in the wire loop due to the time changing magnetic field from the long straight wire?

Related Visualizations

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

• Magnet Falling Through a Conducting Ring
• Faraday's Law

 

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