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

• Athenian
In summary, the conversation discusses the analysis of data from a lab activity on the Zeeman effect, specifically focusing on finding the magnetic field (B) from the given data and how to plot a graph using the areal ratios (delta/Delta). The expert advises against using the data to determine the magnetic field and suggests finding a way to independently measure it. They also mention that the magnetic field is proportional to the current (I) but the constant of proportionality is not mu_0. The conversation ends with the discovery of a calibration curve for the magnetic field, which will be helpful in determining the relationship between B and I.
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!

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?

Athenian said:
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.

Athenian

1. How does the Zeeman Effect affect the magnetic field (B)?

The Zeeman Effect is a phenomenon where the spectral lines of an atom split into multiple lines when placed in a magnetic field (B). This splitting is caused by the interaction between the magnetic field and the electrons in the atom.

2. What is the formula for calculating the magnetic field (B) in the Zeeman Effect?

The formula for calculating the magnetic field (B) in the Zeeman Effect is B = h/λΔλ, where h is the Planck's constant, λ is the wavelength of the spectral line, and Δλ is the difference in wavelength between the split lines.

3. How can the magnetic field (B) be measured in the Zeeman Effect?

The magnetic field (B) can be measured using a device called a magnetometer. This instrument measures the strength and direction of a magnetic field by using a magnetized needle or a digital display.

4. What factors can affect the accuracy of calculating the magnetic field (B) in the Zeeman Effect?

Some factors that can affect the accuracy of calculating the magnetic field (B) in the Zeeman Effect include the precision of the equipment used, the temperature and pressure of the environment, and the presence of any external magnetic fields.

5. Can the Zeeman Effect be used to determine the strength of a magnetic field (B)?

Yes, the Zeeman Effect can be used to determine the strength of a magnetic field (B). By measuring the splitting of spectral lines and using the formula mentioned above, the magnetic field strength can be calculated accurately.

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