Statement; field of current-carrying wire and sheet; units; divergence of B and interpretation.
8.022 Electricity and Magnetism, Fall 2004
Prof. Gabriella Sciolla
Course Material Related to This Topic:
Ampere's Law and its application to determine the magnetic field produced by a current; examples using a thick wire and a thick sheet of current.
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
Course Material Related to This Topic:
Introduction of the Biot-Savart Law for finding the magnetic field due to a current element in a current-carrying 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
Course Material Related to This Topic:
Worked example using the Biot-Savart Law to calculate the magnetic field due to a linear segment of a current-carrying wire or an infinite current-carrying 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
Course Material Related to This Topic:
Uses Biot-Savart Law to determine the magnetic force between two parallel infinite current-carrying wires.
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
Course Material Related to This Topic:
Worked example using the Biot-Savart Law to calculate the magnetic field on the axis of a circular current loop.
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
Course Material Related to This Topic:
Uses Ampere's Law to calculate the magnetic field of an ideal solenoid and of a toroid.
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
Course Material Related to This Topic:
Description and tabular summary of problem-solving strategy for the Biot-Savart Law, with a finite current segment and a circular current loop as examples.
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
Course Material Related to This Topic:
Description and tabular summary of problem-solving strategy for Ampere's Law, with an infinite wire, ideal solenoid, and ideal toroid as examples.
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
Course Material Related to This Topic:
Find the magnetic field everywhere due to a slab carrying a non-uniform current 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
Course Material Related to This Topic:
Find the magnetic field everywhere due to the current distribution in a coaxial cable. 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
Course Material Related to This Topic:
Find the current through a hairpin-shaped wire loop to produce the given magnetic field at a symmetry point. 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
Course Material Related to This Topic:
A long current-carrying wire runs down the center of an ideal solenoid; find the magnetic force on the wire due to the solenoid and find the velocity of a particle inside the solenoid that doesn't feel the field of the wire. 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
Course Material Related to This Topic:
Determine the magnetic field produced everywhere in space around a line segment carrying current. 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
Course Material Related to This Topic:
Determine the magnetic field at the center of an arc of current. 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
Course Material Related to This Topic:
Determine the magnetic field at the center of a rectangle of current. 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
Course Material Related to This Topic:
Determine the magnetic field at the center of a hairpin of current. 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
Course Material Related to This Topic:
Determine the magnetic field along the axis between two infinite wires and determine where the field is the greatest. 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
Course Material Related to This Topic:
Determine the magnetic field everywhere around a wire with a non-uniform current 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
Course Material Related to This Topic:
Determine the magnetic field along the axis between two infinite wires and determine where the field is the greatest. 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
Course Material Related to This Topic:
Find the magnetic field produced by two perpindicular rays of wire. 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
Course Material Related to This Topic:
Describe the application of Biot-Savart and Ampere's Laws; characterize magnetic attraction or repulsion between steady current configurations.
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
Course Material Related to This Topic:
Use Ampere's Law to find the magnetic field due to an infinitely long current-carrying wire; then calculate a circulation involving eight infinite currents and discuss the utility of Ampere's Law.
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
Course Material Related to This Topic:
Find the magnetic field everywhere due to a long, hollow cylindrical conductor carrying a uniform current distribution.
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
Course Material Related to This Topic:
Find the magnetic field everywhere due to a uniform current distribution in a long cylindrical conductor with an off-center cylindrical hole.
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
Course Material Related to This Topic:
Find numerical values for the magnetic field inside and outside an ideal solenoid.
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
Course Material Related to This Topic:
Find the magnetic field at the center of a rotating disk of uniform charge density.
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
Course Material Related to This Topic:
Find the magnetic field at the center of a square configuration of four infinitely long current-carrying wires.
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
Course Material Related to This Topic:
Find the magnetic field of a standard solenoid and compare it to the magnetic field produced by a spinning cylinder with a uniform surface charge.
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
Course Material Related to This Topic:
Identify sign of circulation of magnetic field around a pictured loop.
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
Course Material Related to This Topic:
Explaining in words why parallel currents attract and antiparallel currents repel.
8.02X Physics II: Electricity and Magnetism with an Experimental Focus, Spring 2005
Dr. Peter Dourmashkin, Prof. Gunther Roland
Course Material Related to This Topic:
Finding field of one loop and force exerted on the other.
8.02X Physics II: Electricity and Magnetism with an Experimental Focus, Spring 2005
Dr. Peter Dourmashkin, Prof. Gunther Roland
Course Material Related to This Topic:
Applet showing the magnitude and direction of the magnetic field created by a small segment of current.
8.02T Physics (Electricity and Magnetism) Labs, Spring 2005
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
Course Material Related to This Topic:
Applet demonstrating the method if integrating around a ring of current to find the magnetic field at a point above the ring.
8.02T Physics (Electricity and Magnetism) Labs, Spring 2005
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
Course Material Related to This Topic:
Applet showing the magnitude and direction of the magnetic field at any point in or around a ring of current.
8.02T Physics (Electricity and Magnetism) Labs, Spring 2005
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
Course Material Related to This Topic:
Video animation showing the magnetic field and behavior of two wires with current flowing in the same direction.
8.02T Physics (Electricity and Magnetism) Labs, Spring 2005
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
Course Material Related to This Topic:
Video animation showing the magnetic field and behavior of two wires with current flowing in different directions.
8.02T Physics (Electricity and Magnetism) Labs, Spring 2005
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
Course Material Related to This Topic:
Video animation showing the magnetic field and attraction of two coaxial wire loops with current flowing in the same direction.
8.02T Physics (Electricity and Magnetism) Labs, Spring 2005
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
Course Material Related to This Topic:
Video animation showing the magnetic field and behavior of two coaxial wire loops with current flowing in different directions.
8.02T Physics (Electricity and Magnetism) Labs, Spring 2005
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
Course Material Related to This Topic:
Video animation showing the magnetic field generated by a Helmholtz Coil when the two coils have current flowing in the same direction (magnetic dipole moments aligned).
8.02T Physics (Electricity and Magnetism) Labs, Spring 2005
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
Course Material Related to This Topic:
Video animation showing the magnetic field generated by a Helmholtz Coil when the two coils have current flowing in different directions (magnetic dipole moments anti-aligned).
8.02T Physics (Electricity and Magnetism) Labs, Spring 2005
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
Course Material Related to This Topic:
Interactive applet showing the magnetic field created by two rings with variable position, orientation, size, and current.
8.02T Physics (Electricity and Magnetism) Labs, Spring 2005
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
Course Material Related to This Topic:
Interactive applet simulating the magnetic field and interactions of a current-carrying wire and a compass needle.
8.02T Physics (Electricity and Magnetism) Labs, Spring 2005
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Michael Feld, Prof. Eric Hudson, Prof. John Joannopoulos, Prof. Bruce Knuteson, Dr. George Stephans
Course Material Related to This Topic: