# Gouy Method for Determination of Magnetic Susceptibility

## Determination of Magnetic Susceptibility by Gouy Method

Gouy method is one of the best methods of determining magnetic susceptibility. A powdered sample is taken in a magnetic tube, a sealed thin cylindrical glass tube of 5-10 mm diameter. It is vertically suspended from the beam of the balance between the poles of an electromagnet.

The lower end of the tube is kept in the strong magnetic field of 10,000 gausses and the upper end in a negligible or zero field.

The small force dF exerted on the sample of volume susceptibility χ and small volume dV in the magnetic field H is given as-

dF = H.χ.dV dH/dx

where, dH/dx = field gradient

If a be the cross sectional area of the sample, then-

dV = A.dx

or, dF = H.χ.dV.A.dH

on integrating the above equation, we get-

The force is measured by counterpoising the sample without the magnetic field and then changing weights to restore the balance after the field has been applied. The diamagnetic substances repel lines of force and show less weight while paramagnetic substances attracts lines of force and the sample is pulled down into the gap between the poles of the magnet and show more weight.

Hence,

The quantity 2l/H^{2} is called Calibration constant. It if firstly determined by a standard substance whose χ_{g} is known. The same tube is then used to determine the χ_{g} and χ_{M} of the sample.

χ_{M} = χ_{g} . M

where, M = atomic or molecular weight of the sample.

For paramagnetic substances, the χ_{M} calculated above is corrected for diamagnetic to get χ_{M}^{correct}.

χ_{M}^{correct} = χ_{M} − χ_{diamagnetic}

It is then used to calculate effective magnetic moment, µ_{eff} as-

## Advantages of Gouy Method

✍︎ It requires very simple equipment of reasonable cost, easy to assemble, and it is very simple to operate.

✍︎ Since the amount of sample taken in this technique is quite large, even an ordinary chemical balance can measure the change in mass.

## Disadvantages of Gouy Method

✍︎ Large amount of sample is required.

✍︎ It requires uniform and compact packing of the sample in Gouy tube for correct results. Packing error is ~3–5%.

✍︎ Magnetic susceptibly of sample in the form solution can be determined conveniently.

### Determination of Magnetic Susceptibility by Faraday's Method

### Determination of Magnetic Susceptibility by NMR Method

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