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# 10: Electromagnetism

• 10.1: Relativity Requires Magnetism
Magnetism is a purely relativistic effect. Since relativistic effects are down by a factor of v² compared to Newtonian ones, it’s surprising that relativity can produce an effect as vigorous as the attraction between a magnet and your refrigerator. The explanation is that although matter is electrically neutral, the cancellation of electrical forces between macroscopic objects is extremely delicate, so anything that throws off the cancellation, even slightly, leads to a surprisingly large forc
• 10.2: Fields in Relativity
Based on what we learned in section 10.1, the next natural step would seem to be to find some way of extending Coulomb’s law to include magnetism. For example, we could try to find a formula for the magnetic force between charges q1 and q2 based on not just their relative positions but also on their velocities. The following considerations, however, tell us not to go down that path.
• 10.3: Electromagnetic fields
• 10.4: Transformation of the Fields
• 10.5: Invariants
We’ve seen cases before in which an invariant can be formed from a rank- 1 tensor. The square of the proper time corresponding to a timelike spacetime displacement r⃗ is r⃗ ⋅r⃗ . From the momentum tensor we can construct the square of the mass papa . There are good reasons to believe that something similar can be done with the electromagnetic field tensor, since electromagnetic fields have certain properties that are preserved when we switch frames.
• 10.6: Stress-energy tensor of the electromagnetic field
• 10.7: Maxwell’s Equations
• 10.E: Electromagnetism (Exercises)