For the simple case of a primary solenoid of m turns per metre and a secondary of
turns-area product nA wound on it, the mutual inductance M is µµ0mnA. If the coils contain
a salt with a geometrical filling factor f, then ∆ = (1 + fχ) and if χ = C/T the sensitivity dlnM/dT
is approximately - fC/T2
. For f = 0.5 and C = 0.26 K as for MAS, one therefore requires a
precision ∆M/M of 2 parts in 107
if 1 mK is to be resolved at 25 K.
With a primary current ip of angular frequency ω the solenoidal field H is Mip and the voltage
across the secondary is ipωM or µµ0HnAω. The design of the thermometer and bridge must
be such that this is large enough to achieve the desired sensitivity. Typically µ0H might be
0.1 to 0.3 mT without departing seriously from the zero field limit, and the frequency is
usually between 30 and 300 Hz. Taking 0.2 mT and 100 Hz and a secondary of 500 turns on
a radius of 1 cm, the voltage would be 0.02 volt, 2 parts in 107
of which is 4 nV. This is not
unreasonable, but there is need for caution and the design should aim to provide greater
sensitivity than is indicated by such calculations. While the product nA can be gauged in
advance, the frequency and field may be limited by the effect of eddy currents (roughly
proportional to ω2
H) induced in nearby metallic components. To combat them,