How to Find the Magnetic Field (B) in a Zeeman Effect

[Athenian]

Homework Statement

Refer below.

Relevant Equations

Not sure how relevant this equation is, but the equation below may (or may not) help:

$$\Delta E = \frac{hc}{2\mu t} \bigg(\frac{\delta}{\Delta} \bigg) = \mu_{B} B$$

I have been analyzing a set of data from a lab activity on the Zeeman effect. The data (i.e. images) gathered can be previewed via this Google drive link here.

While I am provided with the numerical data on the current ($I$), I am not provided with any data on the magnetic field. With the given data (i.e. images), I am supposed to graph areal ratios ($\delta/\Delta$) as a function of magnetic field ($B$).

Note that areal ratios ($\delta/\Delta$) are defined as the net change in area between neighboring rings ($\delta$) over the net change in area between neighboring orders ($\Delta$). These areas can be calculated by finding the "distance" of the rings in the images via a software like Gimp.

With the above information in mind, how should I find the magnetic field ($B$) and plot my graph? Or, should I use equations like $B = \mu_{0} I$ to find my answer?

Thank you for reading through this question!

 

[kuruman]

I am unfamiliar with the particular version of the Zeeman effect experiment that you performed. However, it goes against good practice to use your data in order to determine the external magnetic field. That's doing things backward. The magnetic field is your independent variable and there must be a way to independently determine or measure it. The magnetic field B is proportional to the current I but the constant of proportionality is not $\mu_0$. Perhaps you missed it, but there should be a place in the writeup of your lab activity explaining how to find the relation between the field and the current. If there isn't, I recommend that you ask your lab instructor.

 

[Athenian]

Thank you for the clarification. After searching around, there isn't an available equation in the writeup of my lab activity. However, I did end up finding the calibration curve of a magnetic field. I believe this should help?

 

[kuruman]

Thank you for the clarification. After searching around, there isn't an available equation in the writeup of my lab activity. However, I did end up finding the calibration curve of a magnetic field. I believe this should help?

It will help tremendously. Just read the graph to determine what B-field corresponds to what current.