A VISUAL TOUR OF CLASSICAL ELECTROMAGNETISM
A VISUAL TOUR OF CLASSICAL ELECTROMAGNETISM
Produced by
The TEAL/Studio Physics Project
Massachusetts Institute of Technology
For The MIT Course
Physics 8.02:� Electromagnetism
Supported<br>by
The<br>d'Arbeloff Fund for Excellence in MIT Education
The<br>MIT/Microsoft iCampus Alliance
The<br>National Science Foundation
The<br>Helena Foundation
The<br>MIT Classes of 1951, 1955 and 1960
The<br>content contained herein can be freely used and redistributed for non-profit<br>educational purposes, as long as an acknowledgment is given to the MIT TEAL/Studio<br>Physics Project for such use.�
This and additional material will appear in the Spring of<br>2004 on
MIT OpenCourseWare
(http://ocw.mit.edu )
Table of Contents
I.����� Field Theory
II.���� Vector and Scalar Fields
A.��� Scalar Fields<br>and How We Represent Them
1.���� Contour Maps
2.���� Color-Coding
3.���� Relief Maps
B.���� Vector Fields
1.���� Sources and<br>Sinks In Fluid Flows
2.���� Circulation<br>in Fluid Flows
3.���� The Relationship<br>Between Fluid Flow Fields and Electromagnetic Fields
C.��� How We Represent<br>Electromagnetic Vector Fields
1.���� The �Vector<br>Field� Representation of A Vector Field
2.���� The �Field<br>Line� Representation Of A Vector Field
3.���� �Grass Seeds�<br>and �Iron Filings� Representations
4.���� What Is Between<br>The Field Lines?
5.���� The Motion<br>Of Electric and Magnetic Field Lines
III.������ Electrostatics
A.��� Coulomb�s Law<br>and Faraday�s Lines of Force
B.���� The Electric<br>Field
1.���� Definition
2.���� The Electric<br>Field Of A Point Charge And Of A Collection Of Point Charges
3.���� Examples of<br>Electric Fields Due To A Collection Of Charges
a)���� An Electric<br>Dipole
b)���� A Line Of Charge
c)���� A Ring Of Charge
C.��� Stresses Transmitted<br>by Electric� Fields
1.���� Pressures and<br>Tensions
2.���� Examples of<br>Stresses Transmitted By Fields In Electrostatics
a)���� A Charged Particle<br>Moving In A Constant Electric Field
b)���� A Charged Particle<br>At Rest In A Time-Changing External Field
c)���� Like And Unlike<br>Charges Hanging From Pendulums
D.��� Creating Electric<br>Fields
1.���� Creating An<br>Electric Dipole
2.���� Creating And<br>Destroying Electric Energy
E.���� Electric Fields<br>Hold Atoms Together
1.���� Ionic And van<br>der Waals Forces
2.���� A Charged Particle<br>Trap
3.���� An Electrostatic<br>Suspension Bridge
IV.������ Magnetostatics
A.��� The Magnetic<br>Field
1.���� The Magnetic<br>Field Of A Moving Point Charge And Of A Current Element
2.���� The Magnetic<br>Fields Of Charges Moving In A Circle
a)���� Animations<br>of the Magnetic Fields of 1, 2, 4, and 8 Charges Moving In A Circle
b)���� A ShockWave<br>Simulation of the Magnetic Field Of A Ring Of Moving Charges
B.���� Stresses Transmitted<br>By Magnetic Fields
1.���� Pressures and<br>Tensions
2.���� Examples of<br>Stresses Transmitted By Magnetic Fields
a)���� A Charged Particle<br>Moving In A Time-Changing External Magnetic Field
b)���� A Charged Particle<br>Moving In A Constant Magnetic Field
c)���� Forces Between<br>Current Carrying Parallel Wires
d)���� Forces Between<br>Co-axial Current-Carrying Circular Wire Loops
e)���� Torques On<br>A Dipole In A Constant Magnetic Field
V.��� Faraday�s Law
A.��� Time Changing<br>Magnetic Fields Are Always Associated With Electric Fields
B.���� Creating And<br>Destroying Magnetic Energy
C.��� Magnets And<br>Conducting Rings
VI.������ Electromagnetic Radiation
A.��� Dipole Radiation
1.���� An Electric<br>Dipole Varying In Magnitude by 10 %
2.���� An Electric<br>Dipole Completely Reversing
B.���� Radiation From<br>A Quarter Wave Antenna
I.<br>Field Theory
�� In order therefore to appreciate the requirements of<br>the science [of electromagnetism], the student must make himself familiar with<br>a considerable body of most intricate mathematics, the mere retention of which<br>in the memory materially interferes with further progress ��
James Clerk Maxwell [1855]
Classical electromagnetic field theory emerged in more or less complete form<br>in 1873 in James Clerk Maxwell�s A Treatise on Electricity and Magnetism.�<br>Maxwell based his theory in large part on the intuitive insights<br>of Michael Faraday.� The wide acceptance of Maxwell�s<br>theory has caused a fundamental shift in our understanding of physical reality.�<br>In this theory, electromagnetic fields are the mediators of the interaction<br>between material objects.� This view differs radically from the<br>older �action at a distance� view that preceded field theory.��
What is �action at a distance�?� It is a world view in which the<br>interaction of two material objects requires no mechanism other than the objects<br>themselves and the empty space between them.� That is, two objects<br>exert a force on each other simply because they are present.� Any<br>mutual force between them (for example, gravitational attraction or electric<br>repulsion) is instantaneously transmitted from one object to the other through<br>empty space.� There is no need to take into account any method<br>or agent of transmission of that...