# Fields: Long Current-Carrying Wires

## Ampere's Law

Statement; field of current-carrying wire and sheet; units; divergence of B and interpretation.

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## Magnetic Field of a Straight Current-Carrying Wire

Worked example using the Biot-Savart Law to calculate the magnetic field due to a linear segment of a current-carrying wire or an infinite current-carrying wire.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Force Between Parallel Wires

Uses Biot-Savart Law to determine the magnetic force between two parallel infinite current-carrying wires.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Magnetic Field of Two Infinite Currents

Determine the magnetic field along the axis between two infinite wires and determine where the field is the greatest. Solution is included after problem.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Conceptual Biot-Savart and Ampere's Law Questions

Describe the application of Biot-Savart and Ampere's Laws; characterize magnetic attraction or repulsion between steady current configurations.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Ampere's Law with Infinite Currents

Use Ampere's Law to find the magnetic field due to an infinitely long current-carrying wire; then calculate a circulation involving eight infinite currents and discuss the utility of Ampere's Law.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Magnetic Field of Four Parallel Currents

Find the magnetic field at the center of a square configuration of four infinitely long current-carrying wires.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Two Parallel Currents

Do two parallel current-carrying wires attract or repel one another?

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Interactions of Current-Carrying Wires

Explaining in words why parallel currents attract and antiparallel currents repel.

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## Stacked Current-Carrying Loops

Finding field of one loop and force exerted on the other.

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## Magnetic Field of a Current Element

Applet showing the magnitude and direction of the magnetic field created by a small segment of current.

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## Integrating Around a Ring of Current

Applet demonstrating the method if integrating around a ring of current to find the magnetic field at a point above the ring.

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## The Ring of Current

Applet showing the magnitude and direction of the magnetic field at any point in or around a ring of current.

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## Two Wires in Parallel

Video animation showing the magnetic field and behavior of two wires with current flowing in the same direction.

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## Two Wires in Series

Video animation showing the magnetic field and behavior of two wires with current flowing in different directions.

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## Two Rings of Current Attracting

Video animation showing the magnetic field and attraction of two coaxial wire loops with current flowing in the same direction.

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## Two Rings of Current Repelling

Video animation showing the magnetic field and behavior of two coaxial wire loops with current flowing in different directions.

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## Magnetic Field of a Helmholtz Coil (Aligned)

Video animation showing the magnetic field generated by a Helmholtz Coil when the two coils have current flowing in the same direction (magnetic dipole moments aligned).

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## Magnetic Field of a Helmholtz Coil (Anti-Aligned)

Video animation showing the magnetic field generated by a Helmholtz Coil when the two coils have current flowing in different directions (magnetic dipole moments anti-aligned).

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## Two Current-Carrying Rings

Interactive applet showing the magnetic field created by two rings with variable position, orientation, size, and current.

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## The Magnetic Field of a Wire and a Compass

Interactive applet simulating the magnetic field and interactions of a current-carrying wire and a compass needle.

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