# Charge & Coulomb's Law

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## Video Clips

#### Electric Charges (Historical)

RealVideo®
3:01 minutes (4:14 - 7:15)

Knowledge of electrical charges throughout history: Origin of word electron (Greek word for amber); discovery of two types of charge: Positive and negative; like charges repel and unlike charges attract; Ben Franklin discovers conservation of charge, existence of conductors.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Polarization

RealVideo®
12:03 minutes (7:15 - 19:18)

Charging a glass rod with silk, then inducing a polarization of charge in a conductor. Properties of conductors. Demonstration: Using balloons to demonstrate induction of positive and negative charges with conductors and non-conductors.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Charging Through Friction

RealVideo®
6:22 minutes (19:18 - 25:40)

Friction creates a charge when combing your hair, touching a doorknob after walking on a carpet, using Saran™ Wrap and cellophane. Experiment: Beating a student with cat fur to create a charge, then discharging by touching a neon discharge tube.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Van de Graaff Generator

RealVideo®
3:50 minutes (25:40 - 29:30)

Demonstration of a Van de Graaff generator used to charge confetti, causing it to jump in the air.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Electric Force: Coulomb's Law

RealVideo®
6:42 minutes (29:30 - 36:12)

Force of one charge on another charge is Kqq/r^2, unit is Coulomb. A Coulomb is very large, electron has charge 1.6E-19 C. Coulomb's constant K = 9E9 N*m^2/C^2=1/(4pi*ε0). Electrical force between two charges is analogous to force on two masses due to gravity. With 3 or more charges the force on one charge from the other two is the sum of the individual forces.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Human Electroscope

RealVideo®
5:48 minutes (42:00 - 47:48)

Definition of electroscope as a device for measuring charge. Demonstration of human electroscope by charging himself with the Van de Graaff and holding pieces of tinsel.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

## Lecture Notes

#### Coulomb's Law

PDF
Page 48 to page 49
Defines Coulomb's law and calculates an example using a three-charge system.
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

#### History of Electricity

PDF
Page 10 to page 12

Electromagnetism through history; standard model; electric charge.

Prior Knowledge: None
Instructor: Prof. Gabriella Sciolla

#### Coulomb's Law and Superposition

PDF
Page 13 to page 17

Statement; superposition for point charges and distributions; SI vs. cgs units; force from charged rod; Taylor expansions.

Prior Knowledge: Charge
Instructor: Prof. Gabriella Sciolla

#### Work and Energy of Charges

PDF
Page 2 to page 3

Work required to move charge; potential energy of configuration.

Prior Knowledge: Coulomb's Law
Instructor: Prof. Gabriella Sciolla

## Online Textbook Chapters

#### Electric Charge

PDF - 1.0 MB
Page 3

Explanation of electrical charge, with historical background; value of the elementary charge of protons and electrons; includes charge quantization and conservation.

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

#### Coulomb's Law

PDF - 1.0 MB
Page 3 to page 5

Coulomb's Law defined, as well as ε0. Examples of Coulomb's Law are shown with an animation of a Van de Graff generator.

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

#### Principle of Superposition

PDF - 1.0 MB
Page 5 to page 7

Introduces the principle of superposition for electric force and works an example using three charges.

Prior Knowledge: Coulomb's Law (OT2.2)
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

#### Charge, Coulomb's Law, and Electric Field

PDF
Page 14 to page 15

Introduction to charge and how it causes force via Coulomb's Law; description of resulting electromagnetic field.

Prior Knowledge: Vector Fields (OT1.3)
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

#### Electric Field of Two Point Charges

PDF
Problem on page 23

Calculate electric field on axis of two point charges.

Prior Knowledge: Coulomb's Law and Electric Field (OT1.6)
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

#### Hydrogen Atom Forces

PDF - 1.0 MB
Problem on page 29 to page 30

Calculate the strengths of the electromagnetic and gravitational forces between the electron and proton in a hydrogen atom; qualitatively compare to the forces between two planets.

Prior Knowledge: Coulomb's Law and Electric Field (OT1.6), Newton's Law of Gravity
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 Force on an Oil Drop

PDF - 1.0 MB
Problem on page 30 to page 31

Find the mass and charge of an oil drop using electrostatics; solution explains significance of Millikan's oil-drop experiment.

Prior Knowledge: Coulomb's Law and Electric Field (OT1.6)
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

#### Moving Charge in an Electric Field

PDF - 1.0 MB
Problem on page 31 to page 33

Determine the motion and vertical deflection of a charged particle in a constant electric field.

Prior Knowledge: Coulomb's Law and Electric Field (OT1.6)
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

#### Force in a Charge Triangle

PDF - 1.0 MB
Problem on page 40

Determine the electric force on a point charge due to two other charges.

Prior Knowledge: Coulomb's Law (OT2.2)
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

#### Two Charged Pendula

PDF - 1.0 MB
Problem on page 43

Determine the equilibrium separation between two pendula with charged masses; use this to calculate the charge of the masses.

Prior Knowledge: Coulomb's Law (OT2.2)
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

#### Electric Field from Unlike Charges

PDF
Problem on page 9

Identify where the electric field due to a positive and a negative point charge goes to zero.

Prior Knowledge: Coulomb's Law and Electric Field (OT1.6)
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

#### Gravitational and Electric Forces

PDF
Problem 1

Calculating charge necessary for two dust grains to overcome gravitational attraction.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Gravitational and Electric Forces

PDF#
Problem 1

Finding ratio for electron and proton; distance to balance; gravity on large scales.

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

#### Modified Electron Charge

PDF#
Problem 2

Ratio of electric to gravitational forces between earth and moon for smaller electron charge; stable system.

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

## Exam Questions

#### Circle of Point Charges

PDF
Problem 1

Finding force on central point charge before and after an outer charge is removed.

Prior Knowledge: None
Instructor: Prof. Walter Lewin

#### Effect of Two Point Charges

PDF
Problem 1

Finding position of third charge for F = 0; potential energy of third charge and effect of perturbation.

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

#### Third Type of Charge

PDF
Problem 2

Determining experimentally whether an object carries a purported third charge.

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

#### Fields of Point Charges

PDF
Problem 1

For triangular arrangement of charges, finding the E-field, the force on a charge, and the motion of a charge.

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

## Java Applets

#### Molecules

Java Applet
Requires Java Virtual Machine

Video animation showing the interaction of four equal charges: Two positive and two negative. Mention of Pauli and van der Waals forces.

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 Molecules 2D

Java Applet
Requires Java Virtual Machine

Applet simulating the interaction of large numbers of positive and negative charges 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

#### Interactive Molecules 3D

Java Applet
Requires Java Virtual Machine

Applet simulating the interaction of large numbers of positive and negative charges in a three-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

#### Lattices 2D

Java Applet
Requires Java Virtual Machine

Interactive applet simulating the interactions of charged particles 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

#### Lattices 3D

Java Applet
Requires Java Virtual Machine

Interactive applet simulating the interactions of charged particles in a three-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

#### Colliding Lattices

Java Applet
Requires Java Virtual Machine

Interactive applet simulating the behavior of two lattices of charged particles as they collide with one another.

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

#### Charges Interacting Inside a Pentagon-Shaped Box

Java Applet
Requires Java Virtual Machine

Applet simulating the interaction between 10 positively charged particles contained in a pentagon.

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 Capacitor

Java Applet
Requires Java Virtual Machine

Applet simulating the behavior of the charges inside the plates of a parallel plate capacitor.

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 Electrostatic Force Experiment

Java Applet
Requires Java Virtual Machine

Applet simulating the behavior of a conducting sphere placed between the plates of a parallel plate capacitor as it is being charged

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 Electrostatic Zoo

Java Applet
Requires Java Virtual Machine

Interactive applet simulates interaction between charged particles, with ability to view field lines and equipotential lines for the particles.

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 Electrostatic Videogame

Java Applet
Requires Java Virtual Machine

Applet in which the player tries to navigate a simple maze by changing the value of a point charge between positive and negative.

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