Fields & Charge Distributions

 

Electric Dipoles

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

  • 8.02 Physics II: Electricity and Magnetism, Spring 2007
    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

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Continuous Charge Distributions

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

  • 8.02 Physics II: Electricity and Magnetism, Spring 2007
    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

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Electric Field from Continuous Charge Distributions

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

  • 8.02 Physics II: Electricity and Magnetism, Spring 2007
    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

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Electric Potential of Continuous Charge Distributions

Calculating electric potential due to continuous charge distributions using superposition.

  • 8.02 Physics II: Electricity and Magnetism, Spring 2007
    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

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Examples: Potential from Charge Distributions

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

  • 8.02 Physics II: Electricity and Magnetism, Spring 2007
    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

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Problem Solving Strategy: Calculating Electric Potential

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

  • 8.02 Physics II: Electricity and Magnetism, Spring 2007
    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

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Electric Field of a Charged Arc

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

  • 8.02 Physics II: Electricity and Magnetism, Spring 2007
    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

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Electric Field Off Axis of a Charged Rod

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

  • 8.02 Physics II: Electricity and Magnetism, Spring 2007
    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

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Conceptual Questions on Electrostatics

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

  • 8.02 Physics II: Electricity and Magnetism, Spring 2007
    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

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Non-Uniformly Charged Semicircle

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

  • 8.02 Physics II: Electricity and Magnetism, Spring 2007
    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

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Electric Field of a Charged Cylindrical Shell and Filled Cylinder

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

  • 8.02 Physics II: Electricity and Magnetism, Spring 2007
    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

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Electric Potential of an Annulus

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

  • 8.02 Physics II: Electricity and Magnetism, Spring 2007
    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

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Electric Potential of a Charged Rod

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.

  • 8.02 Physics II: Electricity and Magnetism, Spring 2007
    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

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Ellipsoid Conductor

Drawing and explaining electric field near ellipsoid conductor.

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Conducting Cylindrical Shell

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

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Point Charge in a Capacitor

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

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Electric Field of a Dipole

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

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Integrating Along a Line of Charge

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

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The Line of Charge

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

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Integrating Around a Ring of Charge

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

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The Charged Ring

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

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The Force on a Charge in a Time-Changing Field

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

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Creation of a Dipole

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

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Creating an Electric Field

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

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Destroying an Electric Field

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

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Interactive Dipoles

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

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The Ion Trap

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

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Simulation of a Nucleus and Four Electrons

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

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The Suspension Bridge 2D

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.

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The Suspension Bridge 3D

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.

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