# Homework Help: Error Analysis of measured value

1. Mar 11, 2012

### maqdah

1. The problem statement, all variables and given/known data
Alright so i'm writing a lab report and im running into a problem of finding the error on this value.
I am measuring the magnetic susceptibility of a couple of samples. My lab manual and instructor told me the error on the force is related to the error on the derivative of the magnetic field alone and not on the mass or the change in mass.
The trouble is I am measuring the force and calculating the magnetic susceptibility. The value of interest to me is the magnetic susceptibility and I don't know how to get the error on the magnetic susceptibility.

2. Relevant equations
Fx= 0.5/µ0 * χm*m* (dB^2)/(dx)
Thus
χm = (2* Fx* µ0)/(m*(dB^2)/(dx))

3. The attempt at a solution
I know the error on (dB^2)/(dx) and using propagation of error, I calculate the error on the force.
Should I use the propagation of error again to find the error on the magnetic susceptibility with only F and (dB^2)/(dx) contributing to the error??

Edit: I think this should have been in the introductory physics forum, my mistake.

2. Mar 11, 2012

### Dickfore

As it stands, m should be a dimensionless quantity. What does m stand for in your equations?

3. Mar 11, 2012

### maqdah

χm is the mass susceptibility and it has units of m3/kilogram
m is the mass of the sample I am measuring it's susceptibility.

4. Mar 11, 2012

### Dickfore

I have no idea what "mass susceptibility" is. Could you provide a reference from somewhere where this thing is defined?

5. Mar 11, 2012

### maqdah

6. Mar 11, 2012

### Dickfore

OK, so what I knew as magnetic susceptibility is referred to as volume susceptibility. Then, your eqn looks right. m stands for the total mass of the sample.

7. Mar 11, 2012

### maqdah

I know my equation is correct :p Another PF user helped me a lot to get there.
I'm asking about the uncertainty of χm

8. Mar 11, 2012

### Dickfore

So, you have a ratio of 2 experimentally measurable quantities ($F$ and $dB^2/dx$). What is the rule of error propagation when you have a ratio?

9. Mar 11, 2012

### maqdah

Yea, I got that a few minutes ago, I can't believe I was so absent minded :) Thank you for your help. :)

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