# Calculating uncertainty in a experiment

1. Aug 16, 2011

### bobred

1. The problem statement, all variables and given/known data
Finding uncertainty in magnetic field strength. $N=2$, $i=1.00\pm0.005$ A, $R=0.1$ m, $\tan \theta=0.49\pm0.008$

2. Relevant equations
The equation

$B_{coil}=\frac{\mu_0 N i}{2 R \tan \theta}$

3. The attempt at a solution
I am assuming that the radius R and number of turns N are exact.
I know how to find the error when the equation is X=a/b
Should I find this error and scale it by
$\frac{\mu_0 N}{2 R}$?

Last edited: Aug 17, 2011
2. Aug 16, 2011

### mathfeel

For multivariable formula $y = f(x_1, x_2, \dots, x_n)$: $\Delta y^2 = \sqrt{\sum_{j=1}^{n} \left( \frac{\partial f}{\partial x_j} \Delta x_j \right)^2}$

It looks tedious, but try to work out and simplify the algebra before you plug in number.

3. Aug 16, 2011

### PeterO

Your proposal sounds fine to me.

4. Aug 17, 2011

### bobred

Hi

Sorted it out, my problem, I mis-read the formula

$\frac{\delta X}{X}=\sqrt{(\frac{\delta A}{A})^2+(\frac{\delta B}{B})^2}$

For $\delta X$ I needed to have

$\delta X=\sqrt{(\frac{\delta A}{A})^2+(\frac{\delta B}{B})^2} X$

Silly mistake
Thanks