Introduction.:. TOP

Personal Connection:

Magnets served me as a method to keep myself occupied during elementary school. I consistently permanently borrowed my refrigerator's magnets with the goal in mind of making the north sides connect, unfortunately the closest I got was a couple of inches before I was stopped from continuing. My tinkering with magnets over the years evolved into testing their capabilities as projectiles and such. Eventually I moved on from that, but I continued to tinker with magnets creating a relationship with them due to their interesting properties and my own curiosity.

Background:

The magnet is described as a material which has the capability of producing a magnetic field. A magnetic field is treated as the most notable property of a magnet, its description includes “ a force that pulls on other ferromagnetic materials”. Specifically within this internal assessment, the experiments include the use of a permanent magnet instead of a temporary magnet, a permanent magnet differs from the typical magnet because of its longevity, this magnet is made with the help of a material which has been magnetized, the typical example of this includes the refrigerator magnet. When discussing the field geometry, the most commonly known one is a planar, an example of a planar field would be earth, specifically gravity. While within earth's atmosphere gravity's effect on you will remain constant regardless of distance to the ground. While transferring this to a magnetic field, the magnitude won't be constant as a result the formula to calculate will need to be different. An available formula which could be applied would be I/R ; this formula would serve as a method to measure the magnitude of the magnetic force. Although this formula does lack clarity, it's better accustomed to measuring from a line, while in this case the magnetic field sensor will be pointed towards the edge of the magnet. As a result it would require the formula to be altered since it's incapable of giving an accurate product for this experiment, the modification would be simple, overall changing it toI/R^2. This would fall under Coulomb's Law, Coulomb’s Law is a “mathematical description of the electric force between charged objects”, it is believed the size magnitude of the field varies inversely to the distance of the magnet, an example of this would be if the distance is triple from 10 cm to 30 cm, the field should become significantly weaker. Specifically within this experiment, the magnetic field will be recorded based on what extruded from the point/edge of the magnet. This differentiation is important due to the fact of the potential of the point.

Variables:

- Strength of Permanent Magnet: Controlled Variable

- Magnetic Field: Dependent Variable

- Distance: Independent Variable

Statement of Problem:

The purpose of this investigation is to determine the relationship between the distance from the end of a magnet and the magnitude of the magnetic field. As the distance decreases will the strength of the magnetic field shrink at a constant rate.

Hypothesis:

I believe as the distance between the magnet increases the magnetic field produced from it will decrease. This hypothesis is supported by Coulomb's law, which revolve around the formula I/R^2, so as the point of the magnet increases the distance, the magnetic field will shrink.

Method.:. TOP

Diagram of Lab Set Up:

Material included within this experiment consisted of one permanent magnet, Vernier Magnetic Field Sensor, Logger Pro Lab, Mini Quest 2 and one Ruler.

Procedure:

As seen above the materials are laid out, the first step for this study begins once everything has been connected correctly. In order to prevent any error from the beginning, it's beneficial to “zero out” the program, this would prevent it from recording data or being affected before we begin. This step would be completed every time before recording the magnetic field. From here, the student/person would place the north domain of the magnet at their desired distance such as 30 centimeters or 1. This would be followed by starting the program, with the space bar or just the button on the screen. Since the program has begun to collect data, it will approximately take about 10 or less seconds to obtain 100 trials of that specific distance. Once it finishes recording, it's important to highlight the whole graph, by doing so it gives us the option to analyze. Analyzing the data provides us with additional numbers, from here we extract the mean, max and min. Afterwards they would continue the same procedure for each distance up until 30 centimeters.

Raw Data.:. TOP

(Figure 1)

		Magnetic Field
Distance (cm)	Min	Max	Mean
1	5.432	5.44	5.438
2	4.362	4.374	4.368
3	2.305	2.489	2.379
4	1.332	1.5	1.391
5	0.8676	0.993	0.9091
6	0.5885	0.6825	0.628
7	0.4328	0.5113	0.465
8	0.3167	0.3952	0.3478
9	0.234	0.2965	0.2559
10	0.188	0.2352	0.2075
11	0.1452	0.1961	0.1625
12	0.1174	0.1644	0.1362
13	0.09276	0.1358	0.1703
14	0.07701	0.1203	0.09071
15	0.06028	0.1033	0.074422
16	0.05069	0.08981	0.06473
17	0.03838	0.08144	0.05577
18	0.3469	0.06988	0.04666
19	0.031	0.06643	0.04258
20	0.02165	0.05708	0.03559
21	0.01919	0.05462	0.03147
22	0.01599	0.04749	0.02548
23	0.01329	0.04478	0.02474
24	0.01329	0.04478	0.023333
25	0.01033	0.04552	0.02167
26	0.003691	0.038888	0.01621
27	-0.009596	0.02165	0.0004896
28	-0.006889	0.02042	0.003329
29	-0.01009	0.02116	0.001988
30	-0.01476	0.01649	-0.001575

Data File: Excel .:. Text

Data Table.:. TOP

(Figure 2)

Strength of Magnetic Field Over Distance
Distance (cm)	Average (mT)	+/-Uncertainty (mT)
1	5.4380	0.004
2	4.3680	0.006
3	2.3790	0.092
4	1.3910	0.084
5	0.9091	0.063
6	0.6280	0.047
7	0.4650	0.039
8	0.3478	0.039
9	0.2559	0.031
10	0.2075	0.024
11	0.1625	0.025
12	0.1362	0.024
13	0.1703	0.022
14	0.0907	0.022
15	0.0744	0.022
16	0.0647	0.020
17	0.0558	0.022
18	0.0467	0.018
19	0.0426	0.018
20	0.0356	0.018
21	0.0315	0.018
22	0.0255	0.016
23	0.0247	0.016
24	0.0233	0.016
25	0.0217	0.018
26	0.0162	0.018
27	0.0005	0.016
28	0.0033	0.014
29	0.0020	0.016
30	-0.0016	0.016

Data File: Excel .:. Text

The process which allowed me to gain my data was through a computer program, once the magnet is placed at the correct distance, the computer begins recording the magnetic field through a third party device. Its manner of recording includes documenting the field strength a multitude of times, after completing its scans, it combines the data together to create a max, min and mean magnetic field. These three values allow me to create a data table and graph including errors bars. Specifically the error bars were created using the max and minimum values previously mentioned, the formula simply consists of ((maximum – minimun)/2).

Graphs.:. TOP

Graph 1:

(Figure 3)

The graph provided above shows the data points from the data table previously provided

Data File: Excel .:. Text

(Figure 4)

Figure 4 was created using log-log in attempts to linearize the data.

Data File: Excel .:. Text

(Figure 5)

Figure five was created using the original x axis from figure 3 against Y^(1/n) in this case N was extracted from figure 4 the value N is -2.

Data File: Excel .:. Text

Conclusion and Evaluation.:. TOP

After analyzing the data created from this study, it represents an inversely proportional relationship between distance and magnetic field. Regardless of the issues encountered during my study this relationship is still strong and prevalent. The initial formula the study was dependent on is I/R^2 , this formula, when manually calculating the product using this formula and 2r=d, it also represents an inversely proportional relationship. This as a result shows the data collected was accurate on a broad scale, yet it lacks similarity when compared to the data collected. Unfortunately I still lack time and extensive knowledge in magnetic fields and Coulomb's law, in order to accurately distinguish the differences in results. For a future research process, I would enjoy scaling down and focusing on the connection between Coulomb's Law and magnetic fields. This idea is truly interesting to me and worth pursuing since this experiment influenced my curiosity for magnets.

Limitations:

A limitation discovered during this study is the inconsistency of the data, while recording data I noticed clear overlaps from the magnetic field, while the mean of each distance seems to have an inversely proportional relationship to the distance, while referring to the raw data table you’ll begin to notice the overlaps within the maximums and minimums. This later was revealed to become an issue, this was primarily noticed within the graphs. It was efficient and beneficial to remove certain distances from the graph in order to remove any outliers and difficulties when analyzing. This could be due to multiple reasons but currently I lack enough knowledge to be able to accurately deduce the reasoning behind. Some potential reasons could be as small as interference during the recording sessions or a mechanical issue with the equipment which seems unlikely.

Improvements:

The main improvement I would implement in the scenario I reenact this study would be a smaller range. Although it's possible the issues I encountered were unique due to my process, the data I had collected was beneficial for only a margin of the data. Once again referring back to the raw data table the difference in magnetic field after the distance 14 centimeters could be considered negligible depending on the scenario. Another factor which should be considered is location, although unlikely it's possible another magnet creating a magnetic field, some potential culprits could be passing students carrying an object which creates a magnetic field or the possibility of my phone contaminating the data. An additional improvement would be an extension on the original project, by incorporating more trials or varying details such as different magnets it would allow us to test the connection between the magnitude of the magnetic field and distance to a larger degree. For instance by repeating the experiment with multiple magnets it would allow us to cross reference the data from each magnet and create a comprehensive analysis showing the connection between both variables on a larger scale. This would allow us to infer that the inversely proportional relationship is not only limited to this magnet but it's a universal theme throughout the project regardless of varying variables.

Bibliography.:. TOP

“Coulomb's Law.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., 29 Dec. 2022 https:/www.britannica.com/science/Coulombs-law. - This website helped me initially in order to create a solid understanding on magnetic fields specifically the ones revolving around coulombs law.

“Coulomb Force.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., https://www.britannica.com/science/Coulomb-force. - The use of coulombs force was just an insight into a small portion of the project. It serves as the force which created as a result of the magnet

“Coulomb's Inverse Square Law of Magnetism - Explanation, Formulas, Solved Example Problems.” BrainKart, https://www.brainkart.com/article/Coulomb-s-Inverse-Square-Law-of-Magnetism_38445/. – This website serves as an insight into the formulaic part of the project, it also is useful since it contains information from a similar viewpoint.

“Experiment of the Month.” Millersville University, 13 Feb. 1970, https://www.millersville.edu/physics/experiments/023/index.php. – This contains information from a very similar project, it allowed me to look into a project which would help prevent any obvious mistakes from occurring.

“Magnet at a Distance.” Physics Van | UIUC, https://van.physics.illinois.edu/ask/listing/419.. – Once again is just serves as a reliable source which reinforces my project in terms of the formulaic since, since it includes the formula I/r^2.