There are two approaches to measuring paramagnetism that seem to be common. One is to use a balance to measure the slight attraction to a magnet – put sample in a balance, apply magnetic field, look for difference in weight of sample using a Gouy balance or use a torsion balance to observe the attraction in a horizontal plane which takes out the static weight of the sample.

The trouble with these two is the attraction due to paramagnetism is weak compared to the weight of the sample – these are lab bench instruments and the electromagnet consumes a lot of power. Although taking samples of soil is easy enough to bring back to the lab, one really shouldn’t be taking a hammer and chisel to ancient monuments to get a sample for a Gouy balance 😉

The other way of measuring volume magnetic susceptibility is to stick the sample into a coil and measure the inductance – with a different configuration of the coil as a search coil it can be used to measure susceptibility at the rockface.

For a solenoid

*L = µ_{0}µ_{r}N^{2}A/l*

L being the inductance,N the number of turns, A is the cross-sectional area and little l being the length – all of which are constants in any sensor

*µ _{0}* being the permeability of free space,

*µ*

_{0=}4π×10^{-7}N A^{-2}*µ _{r}* is the effective relative permeability of the sample such that

*µ*_{r}*= **χ _{m}*

*+1 where*

*χ _{m}* is the effective magnetic susceptibility of the sample

I suspect this is the method used by the Phil Callahan Soil Meter (PCSM)

Bartington Instruments seem to be the go-to guys for magnetic susceptibility instrumentation. From them I learned that one shouldn’t use too high a frequency, which is a bear, My initial prototype ran at 52kHz which is ten to a hundred times too high.

#### How do you measure the inductance of a coil?

You resonate it with a capacitance and observe the frequency. It’s easy to measure frequency. The obvious way is that of time immemorial – I used a Colpitts oscillator of grid dip oscillator fame

and measured frequency with a frequency counter via a high impedance scope probe (10M/10pf) on the collector of the transistor. A respectably clean sine wave is to be seen

The first thing to note is this is not a big effect – 52,473 Hz unloaded as opposed to 52,441 with the sample. The sensor is a jam jar wound with enamelled wire

From the resonant frequency

f=1/(2π√(LC))

from which I infer the coil was about 0.56mH. Through a whole load of manipulating the formula for inductance

I can derive that if L1 is the inductance of the empty jar and L2 is the inductance of the jar with sample then the effective magnetic susceptibility of the sample *χ _{m}* is (L2-L1)/L1, which I then have to divide by 4π to convert from SI to CGS is about 97

*µCGS[ref]I don’t understand giving units for a dimensionless number, but what the hell I’ll go with Callahan here, and you have to put the micro prefix somehwere[/ref]*. Phil Callahan would not approve…

All volcanic soil & rock is paramagnetic, (from 200 to 2,000 µCGS). According to Dr. Callahan’s research, a soil magnetic susceptibility reading of 0 – 100 µCGS would be poor; 100 – 300 µCGS good; 300 – 800 µCGS very good; & 800 -1200 µCGS above excellent. This force can be added to soil, where it has eroded away, by spreading ground-up paramagnetic rock (basalt, granite, etc.) into the soil.Philip Callahan from the Pike Agri-Lab website

This generally squares with this chart I pinched from Bartington’s manual for the MS2 susceptibility system–

100 will take you to the granites and metamorphic rocks and 800 gets you about halfway to the left hand side.

There again, my sample takes up less than a quarter of the volume of the solenoid I guess, so if it filled the jar it would creep into very good category. That shows one area that needs thought – filling the sample vessel. A look at Bartington’s susceptibility product range of sensors is instructive – it shows me I want something like the MS2F point probe and maybe a search-coil-like MS2D surface scanning probe eventually. Bartington are good enough to tell me the frequency ranges – the MS2F is 580Hz and the MS2D loop is 958Hz – presumably there are issues of getting the inductance high enough for the loop, hence going up in frequency. Or maybe the higher frequency suits the application better – Bartington seem to know their stuff.

#### Room for improvement

- there’s over 20V across the tank circuit, so EMC could be an issue[ref]It’s probably not that bad, the wavelength is in the order of 5km so most of the EMC will be due to the near field, it’s not going to propagate that much[/ref]. This will be even less if I go down in frequency
- The Q of the tank coil is damped by the circuit – I feel bad about the 470 ohm emitter resistor chucked across half the tapped capacitance which has an impedance of -92j at the operating frequency. I will lose sensitivity and pick up long-term drift because of that, though since this is a differential measurement the latter is not such a big deal.
- Form factor – I will usually be taking the sensor to the rock, not the other way round. There’s a sort of assumption that the rock will be bigger than the sensor.

- My frequency is way too high I am an order of magnitude off – Bartington use 4.65kHz and 465 Hz in their MS2product, and indicate the lower frequency is more accurate.

The trouble with dropping frequency is that this is looking for a change at the 5 digit level – 1 part in 10,000. That’s two seconds to get a reading at 4.65 kHz (4650/10000) which is okay, but 20s at the lower frequency.

The obvious solution is to either use a frequency multiplier chain before the frequency measurement, or to put a PLL after it with a ÷N counter in the loop. And put a whole load of turns on the coil to get the inductance up

Go back and do your research, it’s not “dimensionless”. Furthermore your apparently NOT a Farmer, if you were you would understand a PCSM is FAR SUPERIOR to the overpriced bartington system for Famer’s and Grower’s and at a cost they can afford!! You’ll also never realize what makes a PCSM work so well. It’s that it was developed by a couple of incredibly intelligent people, which I guess is what’s so magical about the device!

Crikey, what did I do to rain on your parade?

> Furthermore your apparently NOT a Farmer, if you were you would understand a PCSM is FAR SUPERIOR to the overpriced bartington system for Famer’s and Grower’s and at a cost they can afford!!

Not sure where exactly I claimed to be a farmer 🙂 However, I don’t see why the PCSM and the Bartington system have to not agree, and it seems they do, within the engineering ambition of the PCSM. Surely repeatability is a good thing?

> what makes a PCSM work so well. It’s that it was developed by a couple of incredibly intelligent people, which I guess is what’s so magical about the device!

appeal to authority fallacy detected. It doesn’t matter if the PCSM was developed by Einstein or by 1000 monkeys, all that matters is if it works and agrees with other ways of measuring the same thing. Magical devices may have their place, but probably not here…

Thank you for all the work you put into this project. VEry much appreciated here. I wanted to know how Phillip was able to decree that tensor rings increase paramagnetic energy ans was looking for a way to measure that and I found you. Very interesting.