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Calculating uncertainty in a experiment

  • Thread starter bobred
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  • #1
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Homework Statement


Finding uncertainty in magnetic field strength. [itex]N=2[/itex], [itex]i=1.00\pm0.005[/itex] A, [itex]R=0.1[/itex] m, [itex]\tan \theta=0.49\pm0.008[/itex]

Homework Equations


The equation

[itex]B_{coil}=\frac{\mu_0 N i}{2 R \tan \theta}[/itex]

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
[itex]\frac{\mu_0 N}{2 R}[/itex]?
 
Last edited:

Answers and Replies

  • #2
181
1
For multivariable formula [itex]y = f(x_1, x_2, \dots, x_n)[/itex]: [itex]\Delta y^2 = \sqrt{\sum_{j=1}^{n} \left( \frac{\partial f}{\partial x_j} \Delta x_j \right)^2}[/itex]

It looks tedious, but try to work out and simplify the algebra before you plug in number.
 
  • #3
PeterO
Homework Helper
2,425
46

Homework Statement


Finding uncertainty in magnetic field strength. [itex]N=2[/itex], [itex]i=1.00\pm0.005[/itex] A, [itex]R=0.1[/itex] m, [itex]\tan \theta=0.49\pm0.008[/itex]

Homework Equations


The equation

[itex]B_{coil}=\frac{\mu_0 N i}{2 R \tan \theta}[/itex]

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
[itex]\frac{\mu_0 N}{2 R}[/itex]?

Homework Statement





Homework Equations





The Attempt at a Solution

Your proposal sounds fine to me.
 
  • #4
173
0
Hi

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

[itex]\frac{\delta X}{X}=\sqrt{(\frac{\delta A}{A})^2+(\frac{\delta B}{B})^2}[/itex]

For [itex]\delta X[/itex] I needed to have

[itex]\delta X=\sqrt{(\frac{\delta A}{A})^2+(\frac{\delta B}{B})^2} X[/itex]

Silly mistake
Thanks
 

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