# Fields: Long Current-Carrying Wires

## Video Clips

#### Magnetic Field of Current-Carrying Wire

RealVideo®
4:42 minutes (4:44 - 9:26)

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.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Fields and Forces From Two Current-Carrying Wires

RealVideo®
4:27 minutes (12:53 - 17:20)

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.

Prior Knowledge: Field of Current-Carrying Wire (4:44 of video lecture 11)
Instructor: Prof. Walter Lewin

#### Magnetic Field of a Current Loop

RealVideo®
6:25 minutes (8:52 - 15:17)

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

Prior Knowledge: Magnetic Field of Current-Carrying Wire (4:44 of video lecture 11)
Instructor: Prof. Walter Lewin

#### Demonstration: Magnetic Field of a Wire and a Current Loop

RealVideo®
3:45 minutes (16:54 - 20:39)

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

Prior Knowledge: Magnetic Field of Current-Carrying Wire (4:44 of video lecture 11) and Magnetic Field of a Current Loop (8:52 of video lecture 14)
Instructor: Prof. Walter Lewin

## Lecture Notes

#### Ampere's Law

PDF
Page 7 to page 11

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

Prior Knowledge: Magnetic Forces
Instructor: Prof. Gabriella Sciolla

## Online Textbook Chapter

#### Magnetic Field of a Straight Current-Carrying Wire

PDF - 1.9 MB
Page 4 to page 7

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.

Prior Knowledge: Biot-Savart Law (OT9.1)
Instructors: 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

#### Force Between Parallel Wires

PDF - 1.9 MB
Page 13 to page 14

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

Prior Knowledge: Biot-Savart Law (OT9.1), Force on Current-Carrying Wires in Magnetic Fields (OT8.3)
Instructors: 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

## Practice Problems

#### Magnetic Field of Two Infinite Currents

PDF - 1.9 MB
Problem on page 55 to page 57

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

Prior Knowledge: Biot-Savart Law (OT9.1), Magnetic Field of an Infinite Current (OT9.1 Ex 9.1)
Instructors: 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

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

PDF - 1.9 MB
Problem on page 62

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

Prior Knowledge: Biot-Savart Law (OT9.1), Ampere's Law (OT9.3)
Instructors: 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

#### Ampere's Law with Infinite Currents

PDF - 1.9 MB
Problem on page 63

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.

Prior Knowledge: Ampere's Law (OT9.3)
Instructors: 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

#### Magnetic Field of Four Parallel Currents

PDF - 1.9 MB
Problem on page 65 to page 66

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

Prior Knowledge: Magnetic Field of an Infinite Current (OT9.1 Ex 9.1)
Instructors: 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

#### Two Parallel Currents

PDF
Problem on page 1

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

Prior Knowledge: Magnetic Force Between Two Parallel Currents
Instructors: 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

#### Current Carrying Ribbon

PDF
Problem 3

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

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Interactions of Current-Carrying Wires

PDF
Problem 1

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

Prior Knowledge: None
Instructors: Dr. Peter Dourmashkin, Prof. Gunther Roland

## Exam Questions

#### B-Field from Current-Carrying Wire

PDF
Problem 5

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

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Stacked Current-Carrying Loops

PDF
Problem 4

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

Prior Knowledge: None
Instructors: Dr. Peter Dourmashkin, Prof. Gunther Roland

#### Stacked Current-Carrying Loops

PDF
Problem 5

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

Prior Knowledge: None
Instructors: Dr. Peter Dourmashkin, Prof. Gunther Roland

## Java Applets

#### Magnetic Field of a Current Element

Java Applet
Requires Java Virtual Machine and Shockwave® Player

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

Prior Knowledge: Magnetic Field of a Current-Carrying Wire (pages 6-15 of LS15)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### Integrating Around a Ring of Current

Java Applet
Requires Java Virtual Machine and Shockwave® Player

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

Prior Knowledge: Magnetic Field of a Ring of Current
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### The Ring of Current

Java Applet
Requires Java Virtual Machine and Shockwave® Player

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

Prior Knowledge: Magnetic Field of a Ring of Current
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### Two Wires in Parallel

Java Applet
Requires Java Virtual Machine

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

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### Two Wires in Series

Java Applet
Requires Java Virtual Machine

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

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### Two Rings of Current Attracting

Java Applet
Requires Java Virtual Machine

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

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### Two Rings of Current Repelling

Java Applet
Requires Java Virtual Machine

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

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

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

Java Applet
Requires Java Virtual Machine

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).

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

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

Java Applet
Requires Java Virtual Machine

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).

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### Two Current-Carrying Rings

Java Applet
Requires Java Virtual Machine

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

Prior Knowledge: None
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans