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Homework Help: Magnetic Susceptibility experiment using Faraday method

  1. Mar 3, 2012 #1
    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. Lets 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

     
  2. jcsd
  3. Mar 4, 2012 #2

    tiny-tim

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    hi maqdah! welcome to pf! :smile:

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

    if you must have a cgs answer, just find the magnetic susceptibility in SI, then divide by 4π, see the pf library :wink:
    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, [itex]4\pi[/itex]. To convert cgs values to SI, divide by [itex]4\pi[/itex] for electric susceptibility, and multiply by [itex]4\pi[/itex] for magnetic susceptibility.​
     
  4. Mar 4, 2012 #3
    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?
     
  5. Mar 4, 2012 #4

    tiny-tim

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    hi maqdah! :smile:
    eugh! :yuck: i've never heard of mass susceptibility :confused:

    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 :confused:)
     
  6. Mar 4, 2012 #5
    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.
     
  7. Mar 4, 2012 #6

    tiny-tim

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    yup, i didn't understand your equation …
    … where does it come from? :confused:
     
  8. Mar 4, 2012 #7
    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.
     
  9. Mar 4, 2012 #8

    tiny-tim

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    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? :smile:
     
  10. Mar 4, 2012 #9
  11. Mar 4, 2012 #10

    tiny-tim

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    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! :wink:
     
  12. Mar 4, 2012 #11
    Im not sure I understand. So the equation become Fx = v/(2u0) * χm* dH2/dx?
     
  13. Mar 4, 2012 #12

    tiny-tim

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    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 :wink:
     
  14. Mar 4, 2012 #13
    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.
     
  15. Mar 4, 2012 #14

    tiny-tim

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    yes :smile:
     
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