# Forces: Moving Charges in Magnetic Fields

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## Video Clips

#### Lorentz Force

RealVideo®
5:26 minutes (13:08 - 18:34)

Worked example finding the radius, period, and frequency of the circular motion of an electron in a uniform magnetic field.

Prior Knowledge: Moving Charges in Uniform Fields (1:21 of video lecture 13)
Instructor: Prof. Walter Lewin

#### Demonstration: Electrons in a Uniform Magnetic Field

RealVideo®
5:12 minutes (18:34 - 23:46)

Showing the circular motion of electrons in the magnetic field of a Helmholtz coil using a gas-filled glass tube.

Prior Knowledge: Moving Charges in Uniform Fields (1:21 of video lecture 13)
Instructor: Prof. Walter Lewin

#### Strength of Magnetic Fields

RealVideo®
4:05 minutes (17:20 - 21:25)

Definition, including the Lorentz force on a charge moving in a magnetic field. Definition of Tesla and Gauss units for the strength of a magnetic field.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Demonstration: Distorting a TV Image with a Magnet

RealVideo®
3:30 minutes (21:25 - 24:55)

Explanation of how electrons are used to make image in a TV screen, with a demonstration showing that a magnet will distort this picture when placed near the screen.

Prior Knowledge: Strength of Magnetic Fields (17:20 of video lecture 11)
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

#### Moving Charge in Uniform Magnetic Field

RealVideo®
6:23 minutes (1:21 - 7:44)

Circular motion of moving particles in constant magnetic fields. Finding the radius of the circular path, with an example for an electron moving in a 1T magnetic field.

Prior Knowledge: Lorentz Force (17:20 of video lecture 11)
Instructor: Prof. Walter Lewin

#### Demonstration: Deflecting Electrons with a Magnet

RealVideo®
2:28 minutes (12:29 - 14:57)

Using an electron gun and a magnet to show that the path of an electron will curve in the presence of a magnetic field.

Prior Knowledge: Moving Charge in Uniform Magnetic Field (1:21 of video lecture 13)
Instructor: Prof. Walter Lewin

#### Mass Spectrometer

RealVideo®
5:33 minutes (14:57 - 20:30)

Definition, with examples of use in separating uranium isotopes for the atomic bomb and for separating isotopes for medical radiation treatments.

Prior Knowledge: Moving Charge in Uniform Magnetic Field (1:21 of video lecture 13)
Instructor: Prof. Walter Lewin

#### Cyclotron

RealVideo®
9:10 minutes (20:30 - 29:40)

Definition, with explanation of how a cyclotron is used to accelerate particles with an electric field while containing the particles with a magnetic field. Mention of the use of rings as modern particle accelerators.

Prior Knowledge: Moving Charge in Uniform Magnetic Field (1:21 of video lecture 13)
Instructor: Prof. Walter Lewin

#### Particle Accelerators

RealVideo®
5:02 minutes (29:40 - 34:42)

Pictures and discussion of an early cyclotron as well as two modern examples of particle accelerators: Fermilab and CERN.

Prior Knowledge: Cyclotron (20:30 of video lecture 13)
Instructor: Prof. Walter Lewin

#### Cloud Chambers and Bubble Chambers

RealVideo®
9:50 minutes (34:42 - 44:32)

Definition, with images of their use in making visible the tracks of electrons and other charged particles. Discussion of the discovery of positrons and other new particles.

Prior Knowledge: Cyclotron (20:30 of video lecture 13)
Instructor: Prof. Walter Lewin

#### Demonstration: Cloud Chamber

RealVideo®
4:25 minutes (44:32 - 48:57)

Tracking the motion of electrons and alpha particles in a cloud chamber.

Prior Knowledge: Cloud Chambers (34:42 of video lecture 13)
Instructor: Prof. Walter Lewin

## Lecture Notes

#### Magnetic Forces and Fields

PDF
Page 1 to page 6

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

Prior Knowledge: Electric Fields
Instructor: Prof. Gabriella Sciolla

## Online Textbook Chapters

#### Introduction to Magnetic Fields

PDF
Page 2 to page 4

Introduces the magnetic field created by a bar magnet, and defines the magnetic field through the magnetic force.

Prior Knowledge: None
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

#### Motion of Charged Particles in a Uniform Magnetic Field

PDF
Page 13 to page 15

Mathematical derivation of the circular (or helical) path of a charged particle in a uniform magnetic field.

Prior Knowledge: Magnetic Force (OT8.1-8.2)
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

#### Velocity Selectors and Mass Spectrometers

PDF
Page 15 to page 17

Description of two applications of a uniform magnetic field: velocity selectors and mass spectrometers; introduction to Lorentz force for magnetic and electric fields.

Prior Knowledge: Charges in Uniform Magnetic Field (OT8.5)
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

#### Calculating Cross Products

PDF
Page 19

Reminders and hints for calculating cross products in rectangular coordinates.

Prior Knowledge: None
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

#### Charged Particles in a Magnetic Field

PDF
Problem on page 22

Determine the ratio of the masses of two particles given their radii of curvature in a uniform magnetic field and charge magnitudes. Solution is included after problem.

Prior Knowledge: Motion of Charged Particles in a Uniform Magnetic Field (OT8.5), Mass Spectrometers (OT8.6)
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 Conceptual Questions

PDF
Problem on page 24

Questions 1-3 explore the motion of charged particles in electric and magnetic fields.

Prior Knowledge: Moving Charges in Magnetic Fields (OT8.5)
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

#### Electrons in Earth's Magnetic Field

PDF
Problem on page 24

Find the force on an electron beam in a TV tube, due to Earth's magnetic field, and its total deflection.

Prior Knowledge: Moving Charges in Magnetic Fields (OT8.5)
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

#### A Particle's Trajectory in a Magnetic Field

PDF
Problem on page 26

Characterize the trajectory of a charged particle entering a region of uniform magnetic field.

Prior Knowledge: Moving Charges in Magnetic Fields (OT8.5)
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

#### Particle Orbits in a Magnetic Field

PDF
Problem on page 26 to page 27

Derive the expression for the radius of curvature of a charged particle in a uniform magnetic field and use this to find the mass ratio between two charged particles; also consider adding an electric field.

Prior Knowledge: Moving Charges in Magnetic Fields (OT8.5), Mass Spectrometer (OT8.6)
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

#### Charge Motion in a Magnetic Field

PDF - 1.9 MB
Problem on page 68

Describe the instantaneous radius of curvature for a charged particle in the magnetic field of a nearby current loop.

Prior Knowledge: Magnetic Field of a Current Loop (OT9.1 Ex 9.2a), Motion of Charged Particles in Magnetic Field (OT8.5)
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 and Right Hand Rule

PDF
Problem on page 1 to page 3

Identify the direction of the force on a charged particle moving in a magnetic field.

Prior Knowledge: Magnetic Force
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 Hall Effect Question

PDF
Problem on page 4

Identify the sign of the charge carriers in a Hall effect setup.

Prior Knowledge: Hall Effect
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

#### Parallel Fields

PDF
Problem 1

Describing motion of a particle in parallel E and B fields.

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

#### Resting Electron

PDF
Problem 2

Can a resting electron be set in motion with a constant B-field?

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

#### Motion of an Ion

PDF
Problem 3

Describing trajectory of an ion through E-field, then B-field.

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

#### Nuclei in the LHC

PDF
Problem 3

Finding momentum of nucleus in the Large Hadron Collider and corresponding B-field or E-field.

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

## Exam Questions

#### Radius of Charged Particle Path

PDF
Problem 3

Determining the mass of a particle given its radius of motion in a magnetic field.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Electron in Parallel-Plate Capacitor

PDF
Problem 9

Force on electron; balancing electric and magnetic forces.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Particle in Capacitor and Magnetic Field

PDF
Problem 2

4-part problem; finding E-field, trajectories for particle; computing kinetic energy. Solution not included.

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

#### Magnetic Field Trajectories

PDF
Problem 1

Finding relative charges given trajectories for three particles.

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

## Java Applets

#### The Magnetosphere of the Earth

Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field of the earth as well as the magnetic field of the solar wind, which carries the magnetic field of the sun out to the neighborhood of the earth.

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 Merging

Java Applet
Requires Java Virtual Machine

Video animation demonstrating the process of magnetic merging, which is the cause of solar flares.

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

#### A Bar Magnet in Earth's Magnetic Field

Java Applet
Requires Java Virtual Machine

Applet showing the interaction between the magnetic field lines of the earth and a bar magnet in a classroom at MIT.

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 Moving Positive Charge

Java Applet
Requires Java Virtual Machine

Video animation of the magnetic field created by a moving positive charge.

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 Moving Negative Charge

Java Applet
Requires Java Virtual Machine

Video animation of the magnetic field created by a moving negative charge.

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 One Charge Moving in a Circle

Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field created by a charge moving in a circular path.

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 Two Charges Moving in a Circle

Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field generated by two charges moving in a circular path.

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 Four Charges Moving in a Circle

Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field generated by four charges moving in a circular path.

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 Eight Charges Moving in a Circle

Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field generated by eight charges moving in a circular path.

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

#### Force on a Moving Charge in a Time-Changing Magnetic Field

Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field and force on a charge moving out of the page in a magnetic field that is uniform but changing in strength.

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

#### Charge Moving in a Magnetic Field (Front)

Java Applet
Requires Java Virtual Machine

Video animation showing the motion of a charge moving through a uniform upward magnetic field.

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

#### Charge Moving in a Magnetic Field (Back)

Java Applet
Requires Java Virtual Machine

Video animation showing a back view of the motion of a charge moving through a uniform upward magnetic field.

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 TeachSpin™ Apparatus

Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field and behavior of a magnet suspended by a spring above a current-carrying wire loop.

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 Dip Needle

Java Applet
Requires Java Virtual Machine

Video showing a magnetic dipole moving to align with the magnetic field of the Earth, at a latitude similar to that of Boston.

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 Earth and a Giant Dip Needle (Far)

Java Applet
Requires Java Virtual Machine

Video animation showing a giant magnetic dipole moving to align with Earth's magnetic field.

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 Earth and a Giant Dip Needle (Near)

Java Applet
Requires Java Virtual Machine

Video animation showing a closer view of a giant magnetic dipole moving to align with Earth's magnetic field.

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

#### Magnet Oscillating Between Two Coils

Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field and motion of a magnet between two coils with sinusoidal and out of phase 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

#### Magnet Suspended Between Two Coils

Java Applet
Requires Java Virtual Machine

Video animation showing the magnetic field of a magnet suspended between two coils with currents that are sinusoidal and in phase.

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 Force on a Charge Moving Through a Magnetic Field

Java Applet
Requires Java Virtual Machine

Video animations showing the force felt by a charge moving into and then out of a uniform magnetic field.

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

#### Torque on a Magnetic Dipole in a Constant Field

Java Applet
Requires Java Virtual Machine

Applet simulating the magnetic field of a magnetic dipole which is rotating in a uniform magnetic field.

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