Principle and Working:
Quinck's method is based on the force experienced by a magnetised material in a non-uniform magnetic field and is a version of Gouy's method. It is specially adapted for liquids. On the basis of susceptibility, a substance can be classified as diamagnetic, paramagnetic and ferromagnetic, which is an important observation in material science.
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In the present setup, the liquid moves under the action of the total force F until it is balanced by the pressure exerted over the area A due to a height difference h between the liquid surfaces in the two arms of the U-tube. Allowing for the susceptibility χa and density ρa of the air which the liquid displaces, it follows that,
A (X-Xa).(B2-B02)/2 µ0= Ah (ρ-ρa)g
where g is the acceleration due to gravity, ρ density of liquid, so that
(X-Xa) (B2-B02)=2 µ0h (ρ-ρa)g
by plotting h as a function of B2, the susceptibility χ can be determined directly from the slope of the graph.