1 TITLE

Quinck’s method

2 AIM

Measure the magnetic susceptibility of MnSO4 solution.

3 INTRODUCTION

The Quincke’s method is used to determine magnetic susceptibility of diamag-netic or paramagnetic substances in the form of a liquid or an aqueous solution.When an object is placed in a magnetic field, a magnetic moment is inducedin it. Magnetic susceptibility χ is the ratio of the magnetization I (magneticmoment per unit volume) to the applied magnetizing field intensity H. Themagnetic moment can be measured either by force methods, which involve themeasurement of the force exerted on the sample by an inhomogeneous magneticfield or induction methods where the voltage induced in an electrical circuit ismeasured by varying magnetic moment. The Quincke’s method like the Gouy’smethod belongs to the former class. The force f on the sample is negative ofthe gradient of the change in energy density when the sample is placed

f = ddx [ 12µ0(µr − µra)H2] = 1

2µ0(χ− χa) ddxH

2

Here µ0 is permeability of the free space and µr χ and µraχa are respec-tively relative permeability and susceptibility of the sample and the air whichthe sample displaces. The force acting on an element of area A and length dxof the liquid column is fAdx, so the total force F on the liquid is

F = A∫f(x), ,= Aµ0

2 (χ− χa)(H2 −H20 )

where the integral is taken over the whole liquid. This means that H is equalto the field at the liquid surface between the poles of the magnet and H0 is thefield at the other surface away from the magnet. The liquid (density ρ) movesunder the action of this force until it is balanced by the pressure exerted overthe area A due to a height difference h between the liquid surfaces in the twoarms of the U-tube. It follows that

F = Ah(ρ− ρa)gχ = χa + 2

µ0g(ρ− ρa) H

H2−H20

$

In actual practiceχa, density of air and 0 are negligible and can be ignored.Then the above expression simplifies to

1

χ = 2ρghµ0H2

Hence,by plotting H as a function of H2 the susceptibility χ can be deter-mined directly from the slope of the graph

4 APPARATUS

Quinck’s tube with stand, Sample-Manganese sulphate monohydrate, Travellingmicroscope, Electromagnet, Constant current power supply, Digital gaussmeter.

5 EXPERIMENTAL SETUP

One limb of the U-tube is placed between the pole pieces of an electromagnetsuch that the meniscus of the liquid lies symmetrically between N-S. The lengthof the limb should be sufficient enough to keep the lower extreme end of thislimb well outside the field of the magnet. The rise or fall h on applying the fieldis measured by means of a traveling microscope fitted with a micrometer scaleof least count of order 10−3 cm.

6 EXPERIMENTAL PROCEUDRE

6.1 Magnetc field calibration

• Test and ensure that each unit (Electromagnet and Power Supply) is func-tioning properly

• Scrupulous cleaning of the tube is essential. Thoroughly clean the Quincke’stube, rinse it well with distilled water and dry it (preferably with dry com-pressed air). Do not use the tube for longer than one laboratory periodwithout recleaning it

• Keep the Quincke’s tube between the pole pieces of the magnet as shownin Fig.1. The length of the horizontal connecting limb should be sufficientto keep the wide limb out of the magnetic field.

• Fill the liquid in the tube and set the meniscus centrally within the polepieces as shown. Focus the microscope on the meniscus and take reading

• Apply the magnetic field H and note its value from the calibration, whichis done earlier as an auxiliary experiment. Note whether the meniscus risesup or descends down. It rises up for paramagnetic liquids and solutionswhile descends down for diamagnetics. Readjust the microscope on themeniscus and take reading. The difference of these two readings gives h

2

for the field H. The magnetic field between the poles of the magnet doesnot drop to zero even when the current is switched off. There is a residualmagnetic field R which requires a correction.

• Measure the displacement h as a function of applied field H by changingthe magnet current in small steps. Plot a graph of h as a function of H2

6.2 To find rise in liquid level

• Fix the air gap between the pole pieces of the electromagnet to the mini-mum distance required to insert Quinck’s tube without touching the polepieces.

• Measure the air gap. Each time the air gap changes, the graph will change.

• Mount the Hall probe of the Digital Gaussmeter, DGM-102 in the woodenstand provided and place it at the centre of the air gap such that thesurface of the probe is parallel to the pole pieces. The small black crystalin the probe is its transducer, so this part should be at the centre of theair gap

• Connect the leads of the Electromagnet to the Power Supply, bring thecurrent potentiometer of the Power Supply to the minimum. Switch onthe Power Supply and the Gaussmeter

• Slowly raise the current in the Power Supply and note the magnetic fieldreading in the Gaussmeter

• Plot the graph between the current and the magnetic field. This graph willbe linear for small values of the current and then the slope will decreaseas magnetic saturation occurs in the material of the pole pieces.

7 OBSERVATIONS

7.1 Preparation of solution

7.1.1

Mass of beaker = 113.05gMass of beaker + water = 162.3882gMass of beaker + water + salt = 178.0295gMass of water = 49.3382gMass of dissolved salt = 15.6413g

3

7.1.2

Determination of density ρρ = 1.3172g/cm3

7.2 Magnetic field calibration

I(A) H(Gauss).02 128.07 592.11 242.21 308.39 415.77 646.91 772.95 7871.04 9931.31 16641.65 15511.95 16992.22 18592.50 20392.89 24723.01 22693.50 24693.78 27194.27 2869

4

7.3 Rise of solution level as a function of magnetic field

5

8 CALCULATIONS

From the h vs H2 graphhH2 = 2.052 ∗ 10−6cm2Gauss2

χ = 2ρghµ0H2

χ = 2 ∗ 1.3172 ∗ 980 ∗ 2.052 ∗ 10−6 = 5.29 ∗ 10−3

χ′

sol = χρ = 5.29∗10−3

1.3172 = 4.016 ∗ 10−3 χ′

salt = 4.0165 ∗ 10−3

χ′′

salt = χ′

salt∗molecularweightofsample = 4.0165∗10−3∗169 = .679CGSUnit =679 ∗ 10−3CGSunit

9 RESULT

Value of χ′′

for the sample at laboratory temperature is 679 ∗ 10−3CGSunit

6