Charge to Mass Lab Error Analysis

[DerekSessions]

In a lab measuring the charge to mass ratio of an electron I am having trouble with the error analysis. Specifically, this lab measured the radius of a curved path of an electron in a magnetic field (generated by Helmholtz coils with a a current 'I' running through them) with the velocity of the electron due to an accelerating potential in an anode. My question is about the uncertainty in the final answer. Measurements were taken at 5 set radii, for 3 set accelerating potential, and I measured the current in the Helmholtz coils required to reach the 5 radii at the 3 accelerating potential.

There was uncertainty in the radii, in the accelerating potential, and in the current through the Helmholtz coils. I solved for the charge to mass ratio of each of these 15 measurements (3 accelerating potential for each of the 5 radii) and I propagated error through each of the 15 measurements using:

δ(charge to mass ratio)=(average charge to mass ratio)* √[(δI/I)^2+(δr/r)^2+(δV/V)^2]

(I=current through coils, r=radius, V=accelerating potential)

My issue is, I have 15 measurements for the Charge to mass ratio and the 15 corresponding uncertainties. How do I use these to express the final value in the lab? Because if I use a standard deviation of the 15 measurements, I'm essentially throwing my 15 calculated uncertainties out the window, am I not? Should I not be averaging the 15 measurements for the charge to mass ratio to begin with? Any insight is helpful as I am clearly at a loss.

 

[Greg Bernhardt]

I'm sorry you are not finding help at the moment. Is there any additional information you can share with us?

 

[Khashishi]

All electrons are the same, so you are making duplicate measurements of the same thing, so the uncertainty in your result will decrease as you take more measurements.

I think you take a weighted average of each measurement (weighted by 1/variance) to get the result, and add the inverses of the variances together to get the inverse of the variance of the result.

You should also do a check to make sure that your measurements are reasonably consistent with each other. The standard deviation in the measurements should be similar in scale to your estimated measurement uncertainty for each measurement.