# Fields & Charge Distributions

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## Video Clips

#### Electric Field Between Two Charged Planes

RealVideo®
4:30 minutes (30:05 - 34:35)

Calculating the electric field between two planes with uniform but opposite charges. Diagram of the end effects for the electric field around finite planes of charge.

Prior Knowledge: Gauss's Law for a Plane (23:43 of video lecture 3)
Instructor: Prof. Walter Lewin

#### Demonstration: Electric Field Near a Charged Plane

RealVideo®
7:10 minutes (34:35 - 41:45)

Van de Graaff generator and a large metallic plane used to show that the electric field for a plane falls off much more slowly than the electric field of a sphere of charge.

Prior Knowledge: Gauss's Law for a Plane (23:43 of video lecture 3)
Instructor: Prof. Walter Lewin

#### Demonstration: Electric Field Inside a Charged Sphere is Zero

RealVideo®
6:07 minutes (41:45 - 47:52)

Metallic ping pong balls and a hollow conducting sphere used to show the the electric field inside a uniformly charged sphere is zero.

Prior Knowledge: Gauss's Law for a Sphere (12:50 of video lecture 3)
Instructor: Prof. Walter Lewin

#### Demonstration: Electric Field Between and Around Two Charged Plates

RealVideo®
3:11 minutes (47:52 - 51:03)

A metallic ping pong ball and two charged plates used to show that the electric field between two plates is much stronger than the field around the plates.

Prior Knowledge: Electric Field Between Two Charged Planes (30:05 of video lecture 3)
Instructor: Prof. Walter Lewin

#### Potential in and Around a Hollow Sphere

RealVideo®
7:09 minutes (11:03 - 18:12)

Finding the potential inside and outside of a positively charged hollow sphere. Equipotential surfaces are defined, and compared to contour lines on a map.

Prior Knowledge: Electric Potential (7:14 of video lecture 4)
Instructor: Prof. Walter Lewin

## Lecture Notes

#### Electric Dipoles

PDF
Page 11 to page 23

Definition of electric dipoles and dipole moment; calculation of field due to a dipole; torque on a dipole in an external field.

Prior Knowledge: Electric Field (OT2.4-2.6)
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

#### Continuous Charge Distributions

PDF
Page 24 to page 41

Introduces charge density; problem solving strategy and worked examples calculating electric field due to a charged rod, ring, and disk.

Prior Knowledge: Coulomb's Law (OT2.2), Electric Field (OT2.4-2.6)
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

## Online Textbook Chapters

#### Electric Field from Continuous Charge Distributions

PDF
Page 18 to page 24

Calculations of electric field produced by continuous charge distributions in a rod, ring, and disk.

Prior Knowledge: Charge Density (OT 2.9)
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

#### Electric Potential of Continuous Charge Distributions

PDF
Page 9 to page 10

Calculating electric potential due to continuous charge distributions using superposition.

Prior Knowledge: Superposition of Electric Potential (OT3.3)
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

#### Examples: Potential from Charge Distributions

PDF
Page 13 to page 18

Worked examples showing how to calculate electric potential given continuous charge distributions of a rod, ring, and disk.

Prior Knowledge: Electric Potential of Charge Distributions (OT3.4)
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

#### Problem Solving Strategy: Calculating Electric Potential

PDF
Page 20 to page 21

Step-by-step description of method to determine electric potential from a charge distribution. Examples of ring, rod, and disk are shown.

Prior Knowledge: Electric Potential of Charge Distributions (OT3.4)
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

#### Electric Field of a Charged Arc

PDF - 1.0 MB
Problem on page 36 to page 37

Find the electric field at the center of a uniformly charged semicircle. Solution is included after problem.

Prior Knowledge: Continuous Charge Distribution (OT2.10)
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

#### Electric Field Off Axis of a Charged Rod

PDF - 1.0 MB
Problem on page 37 to page 39

Find the electric field at an arbitrary point due to a finite rod of uniform charge density. Solution is included after problem.

Prior Knowledge: Continuous Charge Distribution (OT2.10)
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 Questions on Electrostatics

PDF - 1.0 MB
Problem on page 39 to page 40

Comparison of gravity and electric forces; field lines crossing; electric field around charges.

Prior Knowledge: Coulomb's Law (OT2.2), Electric Field (OT2.4-2.6), Continuous Charge Distributions (OT2.10)
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

#### Non-Uniformly Charged Semicircle

PDF - 1.0 MB
Problem on page 41 to page 42

Calculate electric force at the center of a non-uniformly charged semicircular wire.

Prior Knowledge: Continuous Charge Distributions (OT2.10)
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

#### Electric Field of a Charged Cylindrical Shell and Filled Cylinder

PDF - 1.0 MB
Problem on page 42 to page 43

Calculate the electric field on axis of a uniformly charged cylindrical shell and a cylinder.

Prior Knowledge: Continuous Charge Distributions (OT2.10)
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

#### Electric Potential of an Annulus

PDF
Problem on page 24 to page 25

Find the electric potential on the symmetry axis of a uniformly charged annulus. Solution is included after problem.

Prior Knowledge: Electric Potential from Charge Distributions (OT3.3-3.4)
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

#### Electric Potential of a Charged Rod

PDF
Problem on page 25 to page 26

Determine the electric potential around a thin rod; use this to determine the work done on a test charge moving around the wire and its velocity. Solution is included after problem.

Prior Knowledge: Electric Potential from Charge Distributions (OT3.3-3.4)
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

#### Electric Field From Charged Disk

PDF
Problem 4

5-part E-field problem; calculating and plotting E-field along z-axis; limiting cases; connection to Coulomb's law.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Ellipsoid Conductor

PDF
Problem 2

Drawing and explaining electric field near ellipsoid conductor.

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

## Exam Questions

#### Charged Cylinder

PDF
Problem 3

4-part problem; finding charge distribution, electric field, and potential for charged cylinder, then again with a dielectric.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Surface and Volume Charge Distribution

PDF
Problem 4

3-part problem; finding E-field above, below, and within a slab of charge with an opposite sheet of charge on top.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Conducting Cylindrical Shell

PDF
Problem 4

Finding and sketching E-field, potential, and potential energy.

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

#### Point Charge in a Capacitor

PDF
Problem 4

5-part problem; finding charge, potential energy, and electric potential.

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

## Java Applets

#### Electric Field of a Dipole

Java Applet
Requires Java Virtual Machine

Interactive applet showing the magnitude and direction of the electric field around a dipole.

Prior Knowledge: Dipoles (pages 11-13 of presentation 2)
Instructors: Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans

#### Integrating Along a Line of Charge

Java Applet
Requires Java Virtual Machine

Applet demonstrating the method of integrating to find the electric field at a point above a line of 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

#### The Line of Charge

Java Applet
Requires Java Virtual Machine

Interactive applet showing the magnitude and direction of the electric field due to a finite line of 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

#### Integrating Around a Ring of Charge

Java Applet
Requires Java Virtual Machine

Applet demonstrating the method of integrating to find the electric field at a point above a ring of 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

#### The Charged Ring

Java Applet
Requires Java Virtual Machine

Interactive applet showing the magnitude and direction of the electric field due to a ring of 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

#### The Force on a Charge in a Time-Changing Field

Java Applet
Requires Java Virtual Machine

Video demonstration of the force on a charge in an electric field that changes over time.

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

#### Creation of a Dipole

Java Applet
Requires Java Virtual Machine

Video demonstrating the creation of an electric dipole by separating a positive and negative charge which were originally in the same spot.

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

#### Creating an Electric Field

Java Applet
Requires Java Virtual Machine

Video showing the creation of a dipole electric field by moving 5 positive charges away from 5 negative charges one-by-one.

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

#### Destroying an Electric Field

Java Applet
Requires Java Virtual Machine

Video showing the destruction of a dipole electric field by moving the positive charges of the dipole toward the negative charges.

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

#### Interactive Dipoles

Java Applet
Requires Java Virtual Machine

Applet simulating the interaction of large numbers of dipoles in a two-dimensional space.

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 Ion Trap

Java Applet
Requires Java Virtual Machine

Interactive applet which simulates the behavior of charged particles in a potential well.

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

#### Simulation of a Nucleus and Four Electrons

Java Applet
Requires Java Virtual Machine

Video demonstrating the formation of an atom from a positive nucleus attracting four electrons.

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 Suspension Bridge 2D

Java Applet
Requires Java Virtual Machine

Applet simulating a series of oppositely charged particles attached to two fixed endpoints, sagging under the weight of gravity. Neutral charges can be dropped onto this arrangement to weigh it down further.

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