Recognition: no theorem link
Demonstration of magnetic dipole-dipole interaction by using smartphone pressure sensor
Pith reviewed 2026-05-12 01:58 UTC · model grok-4.3
The pith
A smartphone pressure sensor in an inflated bag measures repulsive force between neodymium magnets to confirm the inverse fourth power law.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
By recording pressure variations caused by the magnetic repulsion between two fixed-orientation N35 neodymium disc magnets separated by known distances, the setup yields force values whose dependence on separation distance d follows the established inverse-fourth-power relation. Plotting measured force against 1/d to the fourth produces a straight line whose slope directly determines the dipole moment of each magnet, thereby providing experimental confirmation of the theoretical prediction for identical dipoles.
What carries the argument
The smartphone pressure sensor inside an inflated Ziplock bag covered by a glass plate, which converts the vertical magnetic repulsion force into a measurable pressure increase.
If this is right
- The force between two identical magnetic dipoles decreases exactly as the inverse fourth power of their separation distance.
- The magnetic dipole moment of a neodymium disc magnet can be extracted from the slope of a force-versus-1/d^4 plot obtained with consumer-grade pressure sensing.
- The same smartphone-based pressure setup can be used to test other weak repulsive forces in an educational laboratory setting.
Where Pith is reading between the lines
- The approach could be adapted to measure electrostatic repulsion by replacing magnets with charged objects while keeping the bag-and-sensor geometry fixed.
- Logging pressure data continuously through a smartphone app would allow real-time fitting of the 1/r^4 curve during the experiment itself.
- If the glass plate and bag introduce no measurable offset, the technique might be scaled to map the force field around a single magnet by moving the sensor laterally.
Load-bearing premise
The pressure sensor reading inside the inflated bag with glass plate accurately isolates and measures only the magnetic force, with negligible contributions from the bag, plate, air pressure variations, or non-ideal dipole behavior at the tested separations.
What would settle it
Repeating the measurements at multiple distances and finding that a plot of force versus 1/d^4 is not linear, or that the slope-derived dipole moment differs substantially from the accepted value for N35 neodymium magnets, would falsify the claimed confirmation of the inverse-fourth-power relationship.
read the original abstract
In this paper, we present a hands-on activity designed to verify the dependence of the magnetic force between two identical N35 neodymium disc magnets on their separation distance. Utilizing a weight-measuring device incorporating a smartphone pressure sensor placed inside an inflated Ziplock bag, with a glass plate ensuring perfect contact, we measured the magnetic force with high precision. Our results confirm the established inverse fourth power relationship between magnetic force and distance. The linear plot of magnetic force versus the inverse fourth power of distance corroborates the corresponding theoretical model. From the slope of this linear plot, we have calculated the magnetic dipole moment of each magnet, providing a practical validation of theoretical predictions. This methodology also offers an effective approach for educational and experimental verification of magnetic interactions.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper presents a hands-on educational experiment to verify the inverse fourth-power dependence of the magnetic force between two identical N35 neodymium disc magnets on separation distance. A smartphone pressure sensor inside an inflated Ziplock bag with a glass plate is used as a weight-measuring device to record the force; results are reported as a linear plot of force versus 1/r^4 whose slope yields the magnetic dipole moment of each magnet.
Significance. If the measurement isolates the magnetic force with demonstrated accuracy, the work supplies a low-cost, smartphone-based activity that lets students directly test the theoretical r^{-4} scaling for axial dipole-dipole forces and extract a physical parameter, which is valuable for undergraduate or high-school electromagnetism labs.
major comments (3)
- [methods/experimental setup] Experimental setup (methods section): no calibration curve relating pressure-sensor output to known applied forces is provided, nor are zero-magnet baseline runs or controls for bag tension, glass-plate contact, or air-pressure drift described; without these, the claim that the sensor registers only the axial magnetic force cannot be evaluated.
- [results] Results section: the linear plot of force versus 1/r^4 is asserted to confirm the theoretical model, yet no data table, error bars, number of trials, or fit statistics (R^{2}, uncertainties on slope) are shown; this prevents assessment of whether the observed linearity is robust or could be dominated by systematic offsets.
- [analysis/discussion] Dipole-moment extraction (analysis): the slope-to-moment conversion assumes the ideal point-dipole formula holds at the separations used, but no discussion or test of higher-multipole corrections or non-axial alignment errors is given, making the numerical value of the extracted moment difficult to interpret.
minor comments (2)
- [abstract] Abstract claims 'high precision' without any quantitative statement of uncertainty or repeatability.
- [analysis] Notation for the magnetic dipole moment and the exact form of the force law (including the factor of 3/2 or 6/2 for axial configuration) should be stated explicitly when the slope is converted to m.
Simulated Author's Rebuttal
We thank the referee for the constructive and detailed comments. We agree that additional details on calibration, controls, data presentation, and analysis assumptions will strengthen the manuscript and address the concerns raised. We respond to each major comment below and indicate the revisions we will make.
read point-by-point responses
-
Referee: [methods/experimental setup] Experimental setup (methods section): no calibration curve relating pressure-sensor output to known applied forces is provided, nor are zero-magnet baseline runs or controls for bag tension, glass-plate contact, or air-pressure drift described; without these, the claim that the sensor registers only the axial magnetic force cannot be evaluated.
Authors: We agree that these elements are necessary to validate the measurement. In the revised manuscript we will add a calibration curve obtained with known weights, describe zero-magnet baseline runs, and explicitly discuss controls for bag tension, glass-plate contact, and air-pressure drift. These additions will allow readers to assess that the recorded signal corresponds to the axial magnetic force. revision: yes
-
Referee: [results] Results section: the linear plot of force versus 1/r^4 is asserted to confirm the theoretical model, yet no data table, error bars, number of trials, or fit statistics (R^{2}, uncertainties on slope) are shown; this prevents assessment of whether the observed linearity is robust or could be dominated by systematic offsets.
Authors: We acknowledge that the current presentation lacks sufficient quantitative detail. The revised version will include a data table of measured forces versus separation, state the number of trials performed, add error bars to the plot, and report the linear-fit statistics (R^{2} and slope uncertainty). This will enable evaluation of the robustness of the observed linearity. revision: yes
-
Referee: [analysis/discussion] Dipole-moment extraction (analysis): the slope-to-moment conversion assumes the ideal point-dipole formula holds at the separations used, but no discussion or test of higher-multipole corrections or non-axial alignment errors is given, making the numerical value of the extracted moment difficult to interpret.
Authors: The referee correctly notes that the point-dipole approximation requires justification at the distances employed. We will add a discussion of the separation range, an estimate of higher-multipole contributions based on the magnet dimensions, and a description of the alignment procedure used to minimize non-axial errors. A full experimental test of multipole corrections lies beyond the scope of the present educational demonstration; we will note this limitation and suggest it as a possible extension. revision: partial
Circularity Check
No circularity: direct experimental measurement of force vs. distance fitted to known 1/r^4 law
full rationale
The paper measures magnetic force independently using a smartphone pressure sensor inside an inflated bag with glass plate, records values at varying separations, plots force against 1/r^4 to obtain a linear relation, and extracts the dipole moment from the slope of that fit. This is a standard empirical verification and parameter extraction from data; the functional form 1/r^4 is taken from established theory rather than derived or fitted within the paper itself. No self-citations, self-definitional steps, or fitted inputs renamed as predictions appear in the provided text. The central result (linearity confirming the inverse-fourth-power law) is not equivalent to the inputs by construction.
Axiom & Free-Parameter Ledger
axioms (2)
- standard math The force between two identical magnetic dipoles aligned along their axis follows an inverse fourth-power dependence on separation distance.
- domain assumption The smartphone pressure sensor reading, after placement inside the inflated bag with glass plate, provides a direct and accurate proxy for the magnetic force without significant systematic offsets.
Reference graph
Works this paper leans on
-
[1]
https://phyphox.org/sensors/
-
[2]
Castro -Palacio J C, Velazquez -Abad L, Giménez M H and Monsoriu J A 2013 Using a mobile phone acceleration sensor in physics experiments on free and damped harmonic oscillations Am. J. Phys. 81 472–5
work page 2013
-
[3]
Kuhn J and Vogt P 2013 Smartphones as experimental tools: different methods to determine the gravitational acceleration in classroom physics by using everyday devices Eur. J. Phys. Educ. 4 47–58
work page 2013
-
[4]
Salinas I, Monteiro M, Martí A C and Monsoriu J A 2020 Analyzing the dynamics of a Yo - Yo using a smartphone gyroscope sensor Phys. Teach. 58 569–71
work page 2020
-
[5]
Hellesund S 2019 Measuring the speed of sound in air using a smartphone and a cardboard tube Phys. Educ. 54 035015
work page 2019
-
[6]
Pal S K, Sarkar S, and Panchadhyayee P 2024 LiDAR-based determination of spring constant using smartphones The Physics Educator 2450001 (https://doi.org/10.1142/S266133952450001X)
-
[7]
Sarkar S, Pal S K, and Chakrabarti S 2023 Determination of the transverse width and distance of an object with a smartphone camera Phys. Teach. 61 58-61
work page 2023
-
[8]
Pal S K, Sarkar S, and Chakrabarti S 2024 Experimental determination of the transverse width and position of the virtual images produced by thin lenses and a plane mirror with smartphone photography Phys. Teach 62 366–369
work page 2024
-
[9]
Pal S K, Sarkar S, and Panchadhyayee P 2024 Determination of the magnetic moment of a magnet by letting it fall through a conducting pipe Phys. Educ. 59 015022
work page 2024
-
[10]
Pathare S R, Huli S, Lahane R, and Sawant S 2014 Low -cost timer to measure the terminal velocity of a magnet falling through a conducting pipe Phys. Teach. 52 160-164
work page 2014
-
[11]
Zhang C G and Hu S F 2002 Another way to demonstrate Lenz’s law Phys. Teach. 40 249- 249
work page 2002
-
[12]
Wye S 2023 Teaching remote laboratories using smartphone sensors: determining the density of air Phys. Educ. 58 015002
work page 2023
-
[13]
Gkourmpis A 2024 Building a manometer for gases and liquids with a smartphone and a food storage container Phys. Teach. 62 66–67
work page 2024
-
[14]
Chakrabarti S, Pal S K, and Sarkar S 2023 An accurate determination of the refractive indices of water and glass by smartphone photography Phys. Educ. 58 035010
work page 2023
-
[15]
Pal S K, Sarkar S, and Panchadhyayee P 2024 Smartphone -based measurement of magnetic force and demonstration of Newton’s third law of motion Phys. Teach 62 404–405
work page 2024
-
[16]
Chiu M, Guo C, and Treagust D F 2007 Assessing students’ conceptual understanding in science: An introduction about a national project in Taiwan Int. J. Sci. Educ 29 379
work page 2007
-
[17]
Nieminen P, Savinainen A, and Viiri J 2012 Relations between representational consistency, conceptual understanding of the force concept, and scientific reasoning Phys. Rev. ST Phys. Educ. Res. 8 010123
work page 2012
-
[18]
Vokoun D, Beleggia M, Heller L, Sittner P 2009 Magnetostatic interactions and forces between cylindrical permanent magnets J. Magn. Magn. Mater. 321 3758–3763
work page 2009
-
[19]
Beleggia M, Graef M D 2005 General magnetostatic shape –shape interactions J. Magn. Magn. Mater. 285 L1-L10
work page 2005
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.