# How do I find the uncertainty in this specific scenario?

• Hao2k
In summary, the task is to find the uncertainty of the magnetic field, B, using the LINEST function in Excel. The magnetic force, current, and length all have their own uncertainties, while the slope of the resulting line of best fit, LB, also has an uncertainty. The calculation for the uncertainty of B is dB = sqrt(dBm^2 + dBL^2), where dBm is the uncertainty of B due to the slope, m, and dBL is the uncertainty of B due to the length, L. The uncertainty of m, dm, would include uncertainties due to force, current, and fluctuations in the data points on the graph.
Hao2k

## Homework Statement

The task is to find the uncertainty of the magnetic field, B. The magnetic force is plotted against current, so that the slope of the resulting line of best fit is LB, where L is the length of the conductor and theta is constant at 90 degrees (thus sin(theta) = 1). The uncertainty of slope is found using the LINEST function in Excel.

The magnetic force, current, and length all have their own uncertainties while the slope also has a uncertainty.

## Homework Equations

F = ILBsin(theta)

## The Attempt at a Solution

B = m/L
so the uncertainty of B (dB) would be:

dB = sqrt(dBm^2 + dBL^2)

where dBm is the uncertainty of B due to m and dBL is the uncertainty of B due to L.

What I am not sure of, I suppose, is the calculation of dBm. m is the slope of the graph, but it is also F/I, so would that mean that the total uncertainty of m would include both the uncertainty of m due to F and I, and the uncertainty of m due to the fluctuation of the data points on the graph? If so, then would the value of the uncertainty of m be:

dm = sqrt(dmF^2 + dmI^2 + dm_fluc^2)

By the way, sorry if this is the wrong category, because I am unsure of where this goes. Thank you!

If (!) your excel function takes the uncertainties into account properly, you don't have to worry about force and current uncertainties any more.
You'll have to check the documentation what it does.

It is a mathematics question but with strong physics connections. Should work here.

## 1. How do I calculate the uncertainty in my measurement?

The uncertainty in a measurement is typically calculated by taking the standard deviation of multiple measurements and dividing it by the square root of the number of measurements. This will give you the standard error, which is a measure of the uncertainty in your measurement.

## 2. What factors affect the uncertainty in a measurement?

There are several factors that can contribute to the uncertainty in a measurement, including the precision of the instrument used, the skill of the person making the measurement, and any sources of error or variability in the measurement process.

## 3. How do I account for systematic errors in my uncertainty calculation?

Systematic errors, which are consistent errors that occur in the same direction each time a measurement is made, can be accounted for by taking multiple measurements and averaging them. This will help to minimize the impact of these errors on the overall uncertainty in the measurement.

## 4. Can uncertainty be reduced or eliminated?

Uncertainty is inherent in any measurement and cannot be completely eliminated. However, it can be reduced by using more precise instruments, taking multiple measurements, and minimizing sources of error in the measurement process.

## 5. How do I express the uncertainty in my measurement?

The uncertainty in a measurement is typically expressed as a range of values, such as ± 0.5 cm. This indicates that the true value of the measurement is likely to fall within that range with a certain level of confidence. The level of confidence is often expressed as a percentage, such as 95% confidence.

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