How Do You Represent Error in a Log-Log Magnetic Field vs. Distance Graph?

[dfx]

Hi,
I'm investigating the variation of Magnetic Field with Distance. The investigation requires me to plot lnField against lnDistance. My question is, say the quantities had an error of +/- 0.01 mT for the Magnetic Field. How would I represent this on the ln Field v/s ln Distance graph? I intuitively thought it would be ln0.01 but that was obviously wrong as it gave a value of -4.6 ... . Any suggestions?

Also, when sketching lnDistance on the axis, should I make the units on the axis ln(metres) or just metres? And likewise with magnetic field should it be lnTesla or just Tesla? I ask this because when plotting say a quantity against (time) squared, we use the units of (s^2).

Any help very much appreciated. Cheers.

 

[Nate810]

For the error in the magnetic field, you would need to plot a range on the graph that includes the error. For example, if the magnetic field value is mT, then the range for the graph would be from ln(mT-0.01) to ln(mT+0.01). When plotting lnDistance on the axis, you should use ln(metres). Likewise, when plotting magnetic field you should use lnTesla. This is because when plotting a quantity against (time) squared, the units are (s^2).

 

[kyle8921]

Hello,

First of all, it is important to note that when plotting lnField against lnDistance, you are essentially plotting the logarithm of the Magnetic Field and Distance values. This means that the error bars on your graph should also be represented as logarithms, rather than the actual values. In this case, the error of +/- 0.01 mT would be represented as ln(0.01) = -4.605 on the y-axis. This is because the logarithm of a product is equal to the sum of the logarithms of the individual factors. Therefore, ln(0.01 mT) = ln(0.01) + ln(mT) = -4.605 + ln(mT).

As for the units on the axis, it is common practice to use the same units as the quantity being plotted. In this case, the units on the y-axis would be ln(mT) and the units on the x-axis would be ln(m). This is because the logarithm of a unit is still a unit. So, ln(mT) is still a unit of magnetic field and ln(m) is still a unit of distance.

I hope this helps clarify any confusion. Best of luck with your investigation!