Biot-Savart's Law & Ampere's Law

 

Magnetic Field of Current-Carrying Wire

Finding the direction of the magnetic field created by a current-carrying wire, with introduction to the right hand rule and a demo of a compass needle responding to the current through a wire.

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  • Watch video clip from Lecture 11 (4:44 - 9:26)

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Fields and Forces From Two Current-Carrying Wires

Forces felt by two parallel current carrying wires, when the currents are in the same or in opposite directions. Includes a demonstration of these forces.

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  • Watch video clip from Lecture 11 (12:53 - 17:20)

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Magnetic Field of a Current Loop

Finding the magnitude and direction of the magnetic field at the center of a loop of current, with comparison to a dipole field.

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  • Watch video clip from Lecture 14 (8:52 - 15:17)

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Demonstration: Magnetic Field of a Wire and a Current Loop

Using iron filings to view the magnetic field lines near a current-carrying wire and a loop of current.

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  • Watch video clip from Lecture 14 (16:54 - 20:39)

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Ampere's Law

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

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Ampere's Law and its application to determine the magnetic field produced by a current; examples using a thick wire and a thick sheet of current.

  • 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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Biot-Savart Law

Introduction of the Biot-Savart Law for finding the magnetic field due to a current element in a 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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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 a Circular Current Loop

Worked example using the Biot-Savart Law to calculate the magnetic field on the axis of a circular current loop.

  • 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 for a Solenoid

Uses Ampere's Law to calculate the magnetic field of an ideal solenoid and of a toroid.

  • 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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Problem Solving: Biot Savart

Description and tabular summary of problem-solving strategy for the Biot-Savart Law, with a finite current segment and a circular current loop as examples.

  • 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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Problem Solving: Ampere's Law

Description and tabular summary of problem-solving strategy for Ampere's Law, with an infinite wire, ideal solenoid, and ideal toroid as examples.

  • 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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Field of a Non-Uniform Current Slab

Find the magnetic field everywhere due to a slab carrying a non-uniform current density. 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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Magnetic Field of a Coaxial Cable

Find the magnetic field everywhere due to the current distribution in a coaxial cable. 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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Finding Current in a Hairpin Wire Loop

Find the current through a hairpin-shaped wire loop to produce the given magnetic field at a symmetry point. 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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Magnetic Force of a Solenoid and a Long Wire

A long current-carrying wire runs down the center of an ideal solenoid; find the magnetic force on the wire due to the solenoid and find the velocity of a particle inside the solenoid that doesn't feel the field of the wire. 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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Magnetic Field of a Current Segment

Determine the magnetic field produced everywhere in space around a line segment carrying current. 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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Magnetic Field of a Current Arc

Determine the magnetic field at the center of an arc of current. 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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Magnetic Field of a Rectangular Current

Determine the magnetic field at the center of a rectangle of current. 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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Magnetic Field of a Hairpin-Shaped Current

Determine the magnetic field at the center of a hairpin of current. 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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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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Magnetic Field of a Non-Uniform Current Wire

Determine the magnetic field everywhere around a wire with a non-uniform current density. 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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Magnetic Field of a Thin Strip of Current

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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Magnetic Field of Two Semi-Infinite Wires

Find the magnetic field produced by two perpindicular rays of wire. 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 a Hollow Cylindrical Current Distribution

Find the magnetic field everywhere due to a long, hollow cylindrical conductor carrying a uniform current distribution.

  • 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 a Cylindrical Current Distribution with a Hole

Find the magnetic field everywhere due to a uniform current distribution in a long cylindrical conductor with an off-center cylindrical hole.

  • 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 a Solenoid

Find numerical values for the magnetic field inside and outside an ideal solenoid.

  • 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 a Rotating Charged Disk

Find the magnetic field at the center of a rotating disk of uniform charge density.

  • 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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Magnetic Field of a Spinning Cylinder

Find the magnetic field of a standard solenoid and compare it to the magnetic field produced by a spinning cylinder with a uniform surface charge.

  • 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 Ampere's Law Question

Identify sign of circulation of magnetic field around a pictured loop.

  • 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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Current Carrying Ribbon

Finding the magnetic field at points outside and in the plane of the ribbon.

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Interactions of Current-Carrying Wires

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

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B-Field from Current-Carrying Wire

Finding magnetic field using geometry from an arrangement of current-carrying wires.

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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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