# Johnson noise and a magnetic field

1. May 8, 2012

### Isaiah Gray

Would the frequency spectrum of Johnson noise change at all when a magnetic field is applied? My guess is not much, since the field changes only the direction of motion of the electrons, not their speed.

2. May 8, 2012

### Dickfore

Are you interested in Johnson noise in resistors, where the original noise was identified? I am asking because magnetic field is usually applied to Hall probes, which, in turn, are semiconducting. But, there is excess $1/f$ noise in semiconductors.

3. May 8, 2012

### Isaiah Gray

Yes; I am specifically interested in an external magnetic field applied to water and electrolytic solutions.

4. May 8, 2012

### Dickfore

Oh my, this sounds as a pretty complicated problem. The charge transport phenomena in electrolytes are highly non-linear, so a simple conductivity cannot captured the whole physics. Besides, because ions have significant mass, charge transport is coupled to diffusion, as well as thermal conduction. A thermal fluctuation in any of these induces a fluctuation in electric properties. Besides, the geometry of the electrodes might be an important factor.

5. May 8, 2012

### Isaiah Gray

So I guess measuring noise in conductivity wouldn't tell me much then? Man, I just wanted a simple experiment with water and magnetic fields. Maybe if I measured noise in a solid, it would be easier.

6. May 8, 2012

### Dickfore

No, you can do that. There are standard setups for measuring conductivity of electrolytes. Measuring noise refers to measuring fluctuations in voltage drop, however. From an experimental point of view, you need to be clear what you measure. From a theoretical point of view, I think the conductivity is used to express the fluctuations, and, is a more convenient quantity for calculations. Nevertheless, you need to be aware of the physical connection between what you measure and what is used in calculations.

But, when you say water, you have to bear in mind that pure distilled water is actually a very good insulator! The conductivity of an electrolyte is strongly dependent on the concentration.

You asked a question if the spectrum of Johnson noise would change if magnetic field is applied:
1) As far as I know, Johnson noise is specifically referred to metal conductors, where the charge carriers are free electrons. Electrolytes are radically different than this. Therefore, one should not expect the white spectrum to necessarily hold for electrolytes, although it might.

2) Magnetic fields affect ions differently than free electrons, mainly because of the large mass and low mobility of ions.

So, I just wanted to point out these differences.