- 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.

Preparation

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)

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

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.

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

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 *I _{1}* and the outer cylindrical shell carries a current

**Download this video:**

» iTunes U (MP4 - 21MB)

» Internet Archive (MP4 - 21MB)

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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» iTunes U (MP4 - 5MB)

» Internet Archive (MP4 - 5MB)

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)

» Internet Archive (MP4 - 17MB)

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?

**Download this video:**

» iTunes U (MP4 - 35MB)

» Internet Archive (MP4 - 35MB)

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