# Magnetic Susceptibility experiment using Faraday method

• maqdah
In summary, the teacher gave the student an equation for magnetic susceptibility. The student was not able to convert the cgs units to SI units and was having trouble understanding why. After doing some research, the student found that susceptibility has no units but the equation that the teacher gave them still gave them the mass susceptibility in SI units.
maqdah
1. Good day,
Using 4-inch pole caps and a Mettler M5 balance, I got all the values required in order to calculate the magnetic susceptibility of several inorganic compounds such as Manganese (IV) oxide (MnO2). I have the change in mass of the tube with the sample of the compound when the magnetic field is on and when it is off. I got the mass of the sample as well as the region where the gradient of the magnetic field (dH^2/dx) (x being the vertical direction) is constant.
I know my values to be right but I am having a lot of trouble converting to cgs units.

2. Fx= m/2 * μ0 * χm * dH^2/dx
where χm is the mass susceptibility of the sample. 3. Let's take MnO2 as an example,
Fx = Δm*g = 0.0517 grams * 9.81
dH^2/dx = 6.29169 (This is the value of the slope of B^2 in Tesla squared and x in meteres
m= 1.1765 grams

This gives mass/specific susceptibility which is incredibly larger than the literature value (on the order of 10^6)
The literature value of the MOLAR susceptibility is 2280x 10^-6 in cgs units

hi maqdah! welcome to pf!

(try using the X2 and X2 buttons just above the Reply box )
maqdah said:
Fx = Δm*g = 0.0517 grams * 9.81
dH^2/dx = 6.29169 (This is the value of the slope of B^2 in Tesla squared and x in meteres
m= 1.1765 grams

i don't understand why you're converting to cgs, or how exactly you got there

if you must have a cgs answer, just find the magnetic susceptibility in SI, then divide by 4π, see the pf library
cgs (emu) values:

Some books which give values of susceptibility use cgs (emu) units for electromagnetism.

Although susceptibility has no units, there is still a dimensionless difference between cgs and SI values, a constant, $4\pi$. To convert cgs values to SI, divide by $4\pi$ for electric susceptibility, and multiply by $4\pi$ for magnetic susceptibility.​

tiny-tim said:
hi maqdah! welcome to pf!

(try using the X2 and X2 buttons just above the Reply box )i don't understand why you're converting to cgs, or how exactly you got there

if you must have a cgs answer, just find the magnetic susceptibility in SI, then divide by 4π, see the pf library
cgs (emu) values:

Some books which give values of susceptibility use cgs (emu) units for electromagnetism.

Although susceptibility has no units, there is still a dimensionless difference between cgs and SI values, a constant, $4\pi$. To convert cgs values to SI, divide by $4\pi$ for electric susceptibility, and multiply by $4\pi$ for magnetic susceptibility.​

It is true that susceptibility has no units but the equation that I am using gives me the mass susceptibility, which has units of length3/mass. Does what you suggest change?
Also, even if you plug in the numbers, I get a value of magnitude of few 103 instead of something close to 10-6 which begs a question, is my equation even correct in the first place?

hi maqdah!
maqdah said:
… the equation that I am using gives me the mass susceptibility, which has units of length3/mass.

eugh! I've never heard of mass susceptibility

but to convert length3/mass from SI to cgs, you'd multiply by (m/cm)3/(kg/g), = 106/103 = 103

(i haven't followed your calculations, you seem to have mixed SI tesla with cgs grams )

mass susceptibility is just the volumetric susceptibility (the dimensionless quantity) divided by the density of the material. Molar susceptibility is the mass susceptibility multiplied by molar mass.
So now I understood how to convert to cgs units (thanks plenty for that), but I keep getting this feeling that the equation is wrong. Because if you do some dimensional analysis, it just doesn't add up.

maqdah said:
… I keep getting this feeling that the equation is wrong. Because if you do some dimensional analysis, it just doesn't add up.

yup, i didn't understand your equation …
maqdah said:
Fx= m/2 * μ0 * χm * dH^2/dx

… where does it come from?

tiny-tim said:
yup, i didn't understand your equation …

… where does it come from?

The teacher gave it to me in the lab manual. I even found the same equation in other previous published papers that did the same experiment.

hmm …

well, i don't understand why it's H instead of B, i don't understand why H is squared, and i don't understand why there's no charge

can you scan or link to any of those papers?

The first two pictures are the derivation. The equation is in the last picture. Equation 10. χ1 is the susceptibility of the surrounding medium which is air and that can be taken as zero. So we are left with the equation that I wrote.

http://www.freeimagehosting.net/vbkkf
http://www.freeimagehosting.net/6k7ij
http://www.freeimagehosting.net/n6st8

ah!

i] there's no m in there

ii] you're confusing the two different types of magnetic field

H is in amp-turns per metre, not tesla …

if you're using tesla, you need B2o, not µoH2

that's a lot of zeros!

tiny-tim said:
ah!

i] there's no m in there

ii] you're confusing the two different types of magnetic field

H is in amp-turns per metre, not tesla …

if you're using tesla, you need B2o, not µoH2

that's a lot of zeros!

Im not sure I understand. So the equation become Fx = v/(2u0) * χm* dH2/dx?

maqdah said:
Im not sure I understand. So the equation become Fx = v/(2u0) * χm* dH2/dx?

yes, but with B (in tesla) instead of H

so your original χm is multiplied by µ02 times 103/4π

= 4π 10-11 ~ 10-10

tiny-tim said:
yes, but with B (in tesla) instead of H

so your original χm is multiplied by µ02 times 103/4π

= 4π 10-11 ~ 10-10

and the 103/4π is to convert it to cgs units? If yes I understand everything now :)

Thank you so much for your help. I really appreciate it.

maqdah said:
and the 103/4π is to convert it to cgs units?

yes

## 1. What is the purpose of a Magnetic Susceptibility experiment using Faraday method?

The purpose of this experiment is to measure the magnetic susceptibility of a material, which is a measure of how easily it can be magnetized in the presence of an external magnetic field. This can provide valuable information about the composition and properties of the material.

## 2. How does the Faraday method work in this experiment?

In the Faraday method, a sample of the material is placed in a solenoid, which is a coil of wire that produces a magnetic field when an electric current is passed through it. The sample is then subjected to a varying magnetic field, and the resulting induced current is measured using a sensitive ammeter. This current is directly proportional to the magnetic susceptibility of the material.

## 3. What factors can affect the accuracy of the results in a Magnetic Susceptibility experiment using Faraday method?

Several factors can affect the accuracy of the results, including the purity and homogeneity of the sample, the strength and uniformity of the magnetic field, and the precision of the measuring equipment. It is also important to consider any external sources of magnetic interference that may affect the results.

## 4. What are the limitations of using Faraday method for measuring magnetic susceptibility?

One limitation is that this method is only suitable for materials with a relatively small magnetic susceptibility. It is also important to ensure that the sample is not saturated by the magnetic field, as this can affect the accuracy of the results. Additionally, the Faraday method cannot distinguish between paramagnetic and diamagnetic materials, as both types of materials will produce an induced current.

## 5. How is the magnetic susceptibility calculated in a Faraday method experiment?

The magnetic susceptibility (χ) can be calculated using the equation χ = (I/A) x (B/H), where I is the induced current, A is the cross-sectional area of the sample, B is the magnetic field strength, and H is the magnetic field intensity. The units of magnetic susceptibility are dimensionless, but they are often expressed in terms of parts per million (ppm) or in SI units of m^3/kg.