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20. Ampere's Law

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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

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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

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?

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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?

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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?

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» iTunes U (MP4 - 17MB)
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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?

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Related Visualizations

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

 

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