Fields & Charge Distributions

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Video Clips

Video 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)
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Video 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)
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Video 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)
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Video 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)
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Video 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)
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Lecture Notes

Fields (8.02T, Spring 2005)

Document PDF
Page 26 to page 44

Scalar and vector fields, with visual examples. Source, sink, and circulating fluid flow as a vector field, with links to visualizations. Vector field diagrams and field lines, with example of gravitational vector field.

Prior Knowledge: None
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Dipoles (8.02T, Spring 2005)

Document PDF
Page 11 to page 13

Definition, including link to a visualization and mention of the dipole moment.

Prior Knowledge: Electric Charge (pages 45-50 from presentation 1)
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Dipole Fields (8.02T, Spring 2005)

Document PDF
Page 14 to page 18

Electric fields created by dipoles, including the point dipole approximation and a link to a visualization.

Prior Knowledge: Dipoles (pages 11-13 of presentation 2)
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Dipoles in Electric Fields (8.02T, Spring 2005)

Document PDF
Page 19 to page 23

Behavior of dipoles in uniform electric fields, including the torque on the dipole and a link to a visualization.

Prior Knowledge: Dipoles (pages 11-13 of presentation 2)
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Continuous Charge Distributions (8.02T, Spring 2005)

Document PDF
Page 24 to page 41

Method for finding the electric field of charge distributions, including definition of charge density for volume, area, and length. Links to visualizations for finding the electric field of an infinite line of charge and for a ring of charge. Step-by-step calculation of the electric field of a ring of charge. Examples of electric field for a finite line of charge and a disk of charge, with limits of each. Summary of E fields for dipoles, point charges, lines of charge, and planes of charge.

Prior Knowledge: Electric Fields (pages 45-54 of presentation 1)
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Document PDF
Page 1 to page 1

Superposition and charge densities defined, with general equation for calculating electric field due to a continuous charge distribution.

Prior Knowledge: Electric Field (R2)
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Online Textbook Chapters

Dipoles (8.02T, Spring 2005)

Document PDF
Page 11 to page 16

Definition; e-field of dipole and motion of dipole in E-field; potential energy of dipole.

Prior Knowledge: Electric fields
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Document PDF
Page 16 to page 25

Volume, surface, and line charge densities defined; e-fields from rods, rings, disks, and planes.

Prior Knowledge: Electric fields
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Worked Electric Field Problems (8.02T, Spring 2005)

Document PDF
Page 26 to page 39

Strategies and solved E-field problems: Hydrogen atom; Millikan oil drop; motion perpendicular to E-field; e-fields of dipoles, arcs, and finite rods.

Prior Knowledge: Electric fields of charge distributions
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Worked Potential Examples (8.02T, Spring 2005)

Document PDF
Page 13 to page 18

Potential calculated for rods, rings, and disks; e-field from potential.

Prior Knowledge: Electric potential
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Worked Potential Problems (8.02T, Spring 2005)

Document PDF
Page 19 to page 26

Strategies and solved potential problems: Two charges, dipole, annulus, charged wire.

Prior Knowledge: Electric potential
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Worked Gauss's Law Problems (8.02T, Spring 2005)

Document PDF
Page 30 to page 36

Strategies and solved Gauss's Law problems: Parallel planes; flux through flat surface; gravity; potential of sphere.

Prior Knowledge: Gauss's Law
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Creating Electric Fields (8.02T, Spring 2005)

Document PDF - 1.3 MB
Page 26 to page 29

Creating and destroying E-fields by creating or destroying dipoles.

Prior Knowledge: Electric fields
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Practice Problems

Electric Field From Charged Disk (8.02, Spring 2002)

Document 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
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Ellipsoid Conductor (8.02X, Spring 2005)

Document PDF
Problem 2

Drawing and explaining electric field near ellipsoid conductor.

Prior Knowledge: None
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Exam Questions

Charged Cylinder (8.02, Spring 2002)

Document PDF
Problem 3

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

Prior Knowledge: None
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Document 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
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Conducting Cylindrical Shell (8.02X, Spring 2005)

Document PDF
Problem 4

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

Prior Knowledge: None
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Point Charge in a Capacitor (8.02X, Spring 2005)

Document PDF
Problem 4

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

Prior Knowledge: None
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Java Applets

Electric Field of a Dipole (8.02T, Spring 2005)

Java Applet 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)
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Integrating Along a Line of Charge (8.02T, Spring 2005)

Java Applet 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
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The Line of Charge (8.02T, Spring 2005)

Java Applet 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
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Java Applet 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
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The Charged Ring (8.02T, Spring 2005)

Java Applet 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
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Java Applet 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
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Creation of a Dipole (8.02T, Spring 2005)

Java Applet 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
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Creating an Electric Field (8.02T, Spring 2005)

Java Applet 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
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Destroying an Electric Field (8.02T, Spring 2005)

Java Applet 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
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Interactive Dipoles (8.02T, Spring 2005)

Java Applet Java Applet
Requires Java Virtual Machine

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

Prior Knowledge: None
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The Ion Trap (8.02T, Spring 2005)

Java Applet Java Applet
Requires Java Virtual Machine

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

Prior Knowledge: None
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Java Applet Java Applet
Requires Java Virtual Machine

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

Prior Knowledge: None
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The Suspension Bridge 2D (8.02T, Spring 2005)

Java Applet 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
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The Suspension Bridge 3D (8.02T, Spring 2005)

Java Applet Java Applet
Requires Java Virtual Machine

Applet simulating a lattice of positive and negative particles attached to four fixed corners, sagging under the weight of gravity. Neutral charges can be dropped onto this arrangement to weigh it down further.

Prior Knowledge: None
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MIT courses referenced in this section: