20. Ampere'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 review the difference between an open surface and a closed surface.
• To review what is meant by the line integral of a vector around the bounding contour of an open surface.
• To comprehend the meaning of Ampere's Law.
• To be able to explain the meaning of surface current.
• To use Ampere's Law to calculate magnetic fields for an infinite wire, and for an infinite plane.

Learning Objectives

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 9.3 through 9.13:
Sources of Magnetic Fields (PDF - 1.9MB)

Lecture Video

Video Excerpts

Learning Activities

Guided Activities

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

Slides (PDF - 1.7MB)

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)

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: Using Ampere's Law to Find the Field of a Metallic Cylinder and Cylindrical Shell

A solid cylindrical metal conductor has radius a. It is surrounded by a cylindrical conducting metal shell with inner radius b and outer radius c, with a < b < c. The inner conductor carries a current I₁ and the outer cylindrical shell carries a current I₂ in the same direction. The currents are uniformly distributed over the conductors through which they flow. What is the magnetic field is everywhere in space?

Problem 2: Magnetic Field

An infinite wire carrying current I is bent into two lengths perpendicular to each other. One segment runs along the negative x-axis up to the origin, and the other segment extends from the origin down the negative y-axis. What is the magnetic field on the x-axis a distance a from the origin?

Problem 3: Wire with Varying Current Density

A long wire of radius R carries a total current I, with a non-uniform current density J=αr. What is the magnetic field everywhere?

Problem 4: Magnetic Field from Moving Sheets of Charge, and from a Rotating Cylindrical Shell of Charge

A large planar sheet has a charge per unit area σ and moves at speed v. Using Ampere's Law, find the magnetic field everywhere. Suppose there is another sheet parallel to the first one, a distance d away, also carrying charge per unit area σ, but moving at speed -v. Now what is the magnetic field everywhere?

In a separate but related problem, consider a long cylinder of radius a carrying a fixed surface charge σ. The cylinder rotates about its axis at an angular speed ω, in radians per second. What is the magnetic field everywhere?

Related Visualizations

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

• The Magnetic Field of a Current Element
  
• The Magnetic Field of a Moving Positive Charge
• The Magnetic Field of a Moving Negative Charge
• Magnetic Field of Four Charges Moving in a Circle
• Integrating Around a Ring of Current
• The Ring of Current
• Two Wires in Parallel
• Two Wires in Series 
• A Bar Magnet in the Earth's Magnetic Field
• The Magnetic Field of a Helmholtz Coil (aligned)
• Two Rings of Current Attracting
• The Magnetic Field of a Helmholtz Coil (anti-aligned)
• Two Rings of Current Repelling
• The TeachSpin(tm) Apparatus
• Magnet Oscillating Between Two Coils
• Magnet Suspended Between Two Coils

 

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