# Forces: Current-Carrying Wires in Magnetic Fields

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## Video Clips

#### Force on Current-Carrying Wire in a Magnetic Field

RealVideo®
3:27 minutes (9:26 - 12:53)

Finding the force a magnetic field exerts on a current-carrying wire, with a demonstration of a wire jumping in a strong magnetic field.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Forces on Moving Charges and Wires in E and B Fields

RealVideo®
6:45 minutes (24:55 - 31:40)

Finding the force on a moving charge in an electric and magnetic field. Finding the total force on a wire in a magnetic field.

Prior Knowledge: Strength of Magnetic Fields (17:20 of video lecture 11)
Instructor: Prof. Walter Lewin

#### Calculating the Force on a Current-Carrying Wire.

RealVideo®
2:59 minutes (31:40 - 34:39)

Sample calculation of the force on a wire in a magnetic field from a demonstration earlier in the lecture.

Prior Knowledge: Force on Wire in Magnetic Field (24:55 of video lecture 11)
Instructor: Prof. Walter Lewin

#### Motor Contest - Force and Torque on Current Loop

RealVideo®
7:16 minutes (34:39 - 41:55)

Introduction to motor building contest. Discussion of force and torque on a current loop in a magnetic field, with example of current meters in cars.

Prior Knowledge: Force on Wire in Magnetic Field (9:26 of video lecture 11)
Instructor: Prof. Walter Lewin

#### Motor Contest - Making a Motor From a Current Loop

RealVideo®
4:47 minutes (41:55 - 46:42)

Definition of a commutator, with further explanation of the motor contest.

Prior Knowledge: Motor Contest - Force and Torque on Current Loop (34:39 of video lecture 11)
Instructor: Prof. Walter Lewin

#### Demonstration: Motor With Human Commutator

RealVideo®
3:06 minutes (46:42 - 49:48)

Creating a motor from a current loop where the current is manually reversed after every 180° of rotation.

Prior Knowledge: Motor Contest - Force and Torque on Current Loop (34:39 of video lecture 11)
Instructor: Prof. Walter Lewin

## Lecture Notes

#### Build Your Own Electric Motor

PDF
Page 1 to page 2

Overview of project in which students build a motor using little more than magnets, paper clips, a block of wood, and copper wire.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Magnetic Forces and Fields

PDF
Page 1 to page 6

Magnetism from empirical evidence; Lorentz force on charge and wires; Electron trajectories; applications to modern physics; work done by B-fields.

Prior Knowledge: Electric Fields
Instructor: Prof. Gabriella Sciolla

## Online Textbook Chapters

#### Magnetic Force on a Current-Carrying Wire

PDF
Page 4 to page 7

Determines the magnetic force on an arbitrarily shaped current-carrying wire; example considering a semi-circular loop.

Prior Knowledge: Current (OT6.1), Magnetic Force (OT8.1)
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

#### Torque on a Current-Carrying Loop

PDF
Page 8 to page 10

Calculates the torque on a square loop of current in a uniform magnetic field; also defines the magnetic dipole moment.

Prior Knowledge: Torque, Magnetic Force on a Wire (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

#### Rolling Rod

PDF
Problem on page 20 to page 21

Determine the motion of a rolling current-carrying rod in a uniform magnetic field. Solution is included after problem.

Prior Knowledge: Magnetic Force on a Current-Carrying Wire (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

#### Suspended Conducting Rod

PDF
Problem on page 21 to page 22

Calculate the magnetic force required to counteract the force of gravity on a suspended current-carrying rod. Solution is included after problem.

Prior Knowledge: Magnetic Force on a Current-Carrying Wire (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

#### Magnetic Torque on a Current Loop

PDF
Problem on page 24 to page 25

Find the torque on a square current-carrying loop due to a uniform magnetic field, and find the value of current in equilibrium with gravity.

Prior Knowledge: Magnetic Force on a Current-Carrying Wire (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

#### Current-Carrying Bar on an Inclined Plane

PDF
Problem on page 25

Find the current through a bar on an inclined plane in a uniform magnetic field, so that the forces balance.

Prior Knowledge: Magnetic Force on a Current-Carrying Wire (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

#### Magnetic Force on a Wire

PDF
Problem on page 27

Determine the force on a current-carrying wire that is skewed with respect to a magnetic field.

Prior Knowledge: Magnetic Force on a Current-Carrying Wire (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

#### Current Density in a Levitating Wire

PDF
Problem on page 28

Determine the current density and power that are required to make a wire levitate in a magnetic field against the force of gravity.

Prior Knowledge: Current Density (OT6.1), Resistivity (OT6.2), Electrical Power(OT6.3), Magnetic Force on a Current-Carrying Wire (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

#### Force on a Current Loop Near a Current Segment

PDF - 1.9 MB
Problem on page 66

Find the force on a rectangular current loop in the non-uniform magnetic field of a nearby finite current segment.

Prior Knowledge: Magnetic Field of a Current Segment (OT9.1 Ex 9.1), Magnetic Force on Current-Carrying Wires (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

#### Quick Magnetic Force on Wires Questions

PDF
Problem on page 1 to page 5

Identify the direction of the force on a current-carrying wire or loop in the field of a bar magnet.

Prior Knowledge: Magnetic Force on a Current-Carrying Wire
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 Force on Particles

PDF
Problem on page 8

Identify the direction of the force on a moving charged particle due to the magnetic field of another moving charged particle.

Prior Knowledge: Magnetic Force, Magnetic Field of Moving Charges
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 Dipole Movement Questions

PDF
Problem on page 2 to page 5

Characterize the behavior of magnetic dipoles in different magnetic field configurations.

Prior Knowledge: Force on a Magnetic Dipole, Torque on a Magnetic Dipole
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

#### Rail Gun Direction

PDF
Problem on page 8

Find the direction of the magnetic force when a current-carrying rod slides on rails in a uniform magnetic field.

Prior Knowledge: Magnetic Force on 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

#### Voltage in Power Lines

PDF
Problem 1

5-part power problem; finding resistance, power, voltage conditions, and Lorentz force in power lines.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Self-Inductance and Field Energy

PDF
Problem 4

Calculating magnetic field energy and self-inductance of a current-carrying wire.

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

#### Offset of CRT Beam

PDF
Problem 2

Determining the cause of a CRT beam offset slightly to the right.

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

## Exam Questions

#### Loop in a Magnetic Field

PDF
Problem 2

Finding the torque on a current-carrying loop in a magnetic field.

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. Solution not included.

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

#### A Current-Carrying Wire in a Constant Magnetic Field

Java Applet
Requires Java Virtual Machine

Video animation showing a current-carrying wire moving into a uniform magnetic field, then being pushed back out because of the resulting force on the wire.

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

#### The Floating Coil

Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field and behavior of a coil of wire suspended above a magnet, when the current through the wire is flowing in one direction and then the other.

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