Q:

Permittivity, Permeability, and Speed of Light
My physics text book says that Maxwell recognized that the number, reciprocal of [square root of {product of (epsilon naught and mu naught)}] is the speed of light.
How did this happen at his time? At present time, I see on the internet that epsilon and mu naught are both defined in terms of c, the speed of light. They appear to be circularly defined. This means that what Maxwell noticed was obvious. Were they defined the same way during Maxwell’s time also?
If they are circularly defined, (that means epsilon and mu are defined such that they produce speed of light), then isn’t it natural that electromagnetic waves will always have speed of light?

- Subhendu

West Hills, CA, USA

- Subhendu

West Hills, CA, USA

A:

Interesting question.

Back in Maxwell's time, the definitions of permittivity and permeability had no connection with c. The just realted charges to electric field and currents to magnetic fields. After Faraday showed that changing magnetic fields create spatially varying electric fields and Maxwell showed that changing magnetic field create spatially varying electric fields, they gave the relation between the spatial changes and the time changes in a propagating wave. In other words they connected how far with how long, so the speed of the wave could be calculated. The speed of light was already known, and the speeds matched up.

Once that's understood, you can use the theoretical framework to re-express things in terms of c.

Mike W.

Back in Maxwell's time, the definitions of permittivity and permeability had no connection with c. The just realted charges to electric field and currents to magnetic fields. After Faraday showed that changing magnetic fields create spatially varying electric fields and Maxwell showed that changing magnetic field create spatially varying electric fields, they gave the relation between the spatial changes and the time changes in a propagating wave. In other words they connected how far with how long, so the speed of the wave could be calculated. The speed of light was already known, and the speeds matched up.

Once that's understood, you can use the theoretical framework to re-express things in terms of c.

Mike W.

*(published on 06/18/2010)*