# Propagation of uncertainty calculations

1. Sep 30, 2006

### leright

I hope this is the right place for this...

Well, I have a lab where we measured the charge/mass ratio of an electron using a helmholtz coil and vacuum tube. I need to calculate the propagation of uncertainty in my final value. The formula for calculating the e/m ratio is the following...

e/m = (2.47E12(a^2/N^2))*(V/((I^2)*r^2))), where a is the radius of the coil that produces the B-field, N is the number of turns in the coil, V is the electron accelerating voltage, I is the coil current, and r is the radius of curvature of the electron beam.

Now, when I calculate the propagation of uncertainty the factor 2.47E12 makes the uncertainty very large and the percent uncertainty is around 50%. What do I do about that huge number??

Thanks.

2. Sep 30, 2006

### leright

3. Sep 30, 2006

### Staff: Mentor

The constant 2.47E12 should give large uncertainties since the uncertainties are of small numbers themselves.

What formula are you using for propagation of uncertainties?

Last edited: Sep 30, 2006
4. Sep 30, 2006

### leright

well, it does give large uncertainties.

This is the formula I always use...

The second formula that is.

5. Sep 30, 2006

### Staff: Mentor

Well that is the correct formula.

What are the uncertainties of each of the values? For example, the number of turns in the coil should have no uncertainty. If the uncertainties are on the order of a few percent of 4 parameters, a, V, I and r, then one might get a 50% error, but if the uncertainties are fractions of a percent, then I would suspect a mathematical error.

What is the largest uncertainty? If a single uncertainly is large, then one would have to reduce the uncertainty with a better measurement or better device.

Last edited: Sep 30, 2006
6. Sep 30, 2006

### leright

All of the uncertainties are reasonably small, but when you take the derivative of the e/m equation that huge constant is still there.......the uncertainties of the measurements are not small enough to balance it out....