Practice question · Put in order
Arrange these steps in the logical order by which Maxwell’s equations predict light.
- Note that a changing E drives B and a changing B drives E
- Identify the resulting speed with the measured speed of light
- Add the displacement current to make Ampère’s law consistent
- Combine the two curl equations into a wave equation
Hints
- The chain starts with fixing an inconsistency, not with waves.
- The identification with light comes last, once the speed has been computed.
Show the answer
- Add the displacement current to make Ampère’s law consistent
- Note that a changing E drives B and a changing B drives E
- Combine the two curl equations into a wave equation
- Identify the resulting speed with the measured speed of light
Why
The displacement current comes first, purely to fix an inconsistency. Its symmetry with Faraday’s law then permits combining the two into a wave equation, whose speed turns out to match light, a prediction, not an assumption.
Practise Maxwell’s Equations and Electromagnetic Waves
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