Johnson-Nyquist noise of an inductor

[olaney]

Homework Statement

Although it's easy to find calculations of thermal noise for resistors and capacitors, the equivalent for inductors is not found. What is the relevant formula? Is there some simple conversion for this?

Homework Equations

The Attempt at a Solution

 

[tech99]

A perfect inductor is a pure reactance. Therefore it can store energy but it cannot absorb it. The energy will come out again when the field collapses. As the inductor cannot absorb energy, it cannot generate it either. It is like a shiny surface in heat radiation. So no noise from a perfect inductor.
No noise from a perfect capacitor either.
With a practical inductor, there is resistance, so you just take the noise EMF across the resistance and consider it in series with the inductance.

 

[olaney]

Capacitors do have thermal noise, see for instance the wikipedia article for Johnson-Nyquist noise. By the same reasoning so will an inductor.
In the case of an inductor, yes there is series resistance, but I'm interested in the noise associated with the inductance alone.

 

[tech99]

Capacitors do have thermal noise, see for instance the wikipedia article for Johnson-Nyquist noise. By the same reasoning so will an inductor.
In the case of an inductor, yes there is series resistance, but I'm interested in the noise associated with the inductance alone.

Thank you very much for drawing my attention to this.
It appears that a pure reactance will develop a noise voltage but cannot deliver noise power.

 

[olaney]

In thinking more about this, it makes sense that just as capacitor noise is a voltage in the open circuit condition, inductors should have current noise in the short circuit condition. This will apply even for zero resistance as it's just the electrons randomly sloshing back and forth at temperature. I'm just surprised there's nothing in the literature beyond some arm waving generalities. Sounds like a master's thesis for someone with the time and inclination.