Measuring Earth’s Magnetic Field Usinga Smartphone Magnetometer

Simen HellesundUniversity of Oslo

Abstract

I use the magnetometers of a smartphone to measure the magnitude of the earth’s mag-netic field. A method for eliminating bias due to internal magnetic fields in the phone isproposed.Keywords: Earth’s magnetic field, magnetometer, Hall-effect.

Introduction

In recent years, modern smartphones havebecome packed with sensors: Accelerom-eters, gyroscopes, microphones, cameras,proximity sensors, and more. Most peopleare walking around with a potential lab-oratory in their pocket, the like of whichwould have been the envy of any experi-menter in times gone by. In recent years,numerous papers have been published de-scribing smartphone-based experiments foreducational purposes, utilising the varioussensors of the smartphone [1–7].Magnetometers, sensors for measuring

magnetic fields, have become ubiquitousin smartphones. These magnetometers arewhat enables the phone’s compass to func-tion. Several papers have also been pub-lished describing how such sensors could beused in education [8–11].The magnetometers used in smartphones

utilise the so-called Hall-effect to operate.

This effect was first demonstrated by Ed-win Hall in 1879. When a current is flowingthrough a thin foil of semiconductor mate-rial, a voltage difference will arise perpen-dicular to the direction of the current in thepresence of a magnetic field perpendicularto the semiconductor foil [12]. This voltageis linearly dependent on the strength of themagnetic field. Today, the material neededto make a Hall-sensor sensitive enough tomeasure the strength of the earth’s mag-netic field is small enough to fit inside amobile phone. Most phones will, in fact,contain three magnetometers, one for eachspatial direction.There are a plethora of apps available

for accessing the instantaneous readings ofa phone’s magnetometer. For this experi-ment, the app named Physics Toolbox Mag-netometer [13], available in the Google Playstore, is used. The simplest way of measur-ing the field strength of the earth’s mag-netic field would be to simply take the vec-

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tor sum of the field strength contributionsin each spatial direction. This is done au-tomatically in the Physics Toolbox Magne-tometer app. However, when testing theapp with the smartphone used in this exper-iment, I observe that the physical orienta-tion of the phone has a noticeable effect onthe field strength readings. This indicatesthe presence of systematic offsets in themagnetometer sensors, or constant mag-netisation of the phone. I suggest a methodto eliminate these effects, thus achieving amore accurate measurement.

Experimental Setup

The only equipment needed to perform theexperiment is a smartphone with a mag-netometer app installed. The phone usedhere is a Motorola Moto g6 Plus, shown inFigure 1. The approximate location of themagnetometer sensors in the phone is de-termined by moving a test magnet acrossthe surface of the phone. The magnetome-ter reading spikes at the closest approachof the test magnet to the magnetometer.The approximate location of the sensors ismarked in blue in the Figure. This locationis not critical to the experiment.The coordinate system of the magne-

tometer app is as follows: The positive x-direction is defined as pointing directly leftto right in the plane of the phone screen.The y-direction also lies in this plane and ispointing directly upwards along the screen.The z-direction is perpendicular to the x-y-plane and is pointing directly out of thescreen. This coordinate system is drawn inFigure 1.

Figure 1: Experimental setup. The tripodseen in the picture was not usedin the experiment.

Procedure

As mentioned in the previous section, themagnetic field strength reading of the mag-netometer app is found to be quite stronglydependent on the orientation of the smart-phone. This means that the magnetic fieldmeasured by the magnetometer will be thesum of the earth’s magnetic field Bearth andthe constant magnetic offset Boffs in thephone:

Bmeas = Bearth +Boffs . (1)

If the phone is flipped such that the mag-netic field is measured in the opposite di-rection, the offset term will be the same,but the sign on the contribution from theearth’s magnetic field will change:

Bπmeas = −Bearth +Boffs . (2)

The constant offset Boffs can be eliminatedby adding Equations 1 and 2. The magnetic

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field of the earth is then taken as the meanof the two measurements:

Bearth =Bmeas +Bπ

meas

2. (3)

The smartphone contains three magne-tometers, one for each spatial direction. Tominimise the effect of potential miscalibra-tion of any one of the sensors, the mea-surement is performed individually for eachsensor. This is done by orienting the smart-phone such that only the magnetometer inquestion has a reading.I was not able to find any information

on the resolution of the analog to digitalconverter of the magnetometers. This un-certainty is assumed to be lower than thereadout uncertainty of the measurement;as I am not able to hold the phone com-pletely still during the measurement, thefield strength reading fluctuates somewhat.The field strength is thus determined to thenearest µT.The experiment was first performed in-

doors. This yielded inconsistent results,possibly due to a permanent magnetisationof the building in which the experiment wasdone. Iron rebars in the concrete of thebuilding, for example, may have obtained apermanent magnetisation. The experimentwas therefore moved outside.The experiment was also first performed

by attaching the phone to a camera tripod,using a clamp. The tripod allows for ac-curate orientation of the phone in all di-rections. The tripod used can be seen inFigure 1. However, the metal legs of thetripod were found to be magnetised. Thismagnetisation interfered with the measure-ments. The tripod was therefore aban-doned in favour of simply orientating thephone by hand.

Results

The results of the measurements can befound in Table 1. Two measurements areperformed for each magnetometer accord-ing to the procedure described in the pre-vious section. Taking the average of eachsuch pair of measurement removes the con-stant offset due to internal magnetic fieldsin the phone. This gives one value forthe magnetic field strength of the earthfor each magnetometer. These values arestored in Table 2. Taking the average ofthese three measurements gives the finalmeasurement of the earth’s magnetic field:Bearth = 50.5± 0.4 µT. The uncertainty onthe measurement is found by adding the un-certainties on the individual measurementsin quadrature. The field strength obtainedis reasonable for Oslo, Norway, where theexperiment is performed.

Direction Bmeas [µT]x 47±1xπ −53±1y 51±1yπ −52±1z 51±1zπ −49±1

Table 1: Magnetic field strengthmeasurements.

Measurement (dir.) Bearth [µT]1 (x) 50.0±0.72 (y) 51.5±0.73 (z) 50.0±0.7

Table 2: Magnetic field strength measure-ment. Averaging out constantoffsets.

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Conclusion

In this article, I demonstrate an economicexperiment for measuring the earth’s mag-netic field. The only equipment needed is asmartphone with magnetometer sensors. Amethod is shown to eliminate the effect ofinternal magnetic fields in the phone.Students taking an experimental course

on electromagnetism can, for example, usethis method along with other methods formeasuring the earth’s magnetic field, tocheck their results. The experiment alsoprovides an opportunity for students topractice estimating uncertainties and sys-tematic errors.Steps should be taken to perform the ex-

periment away from any potential sourcesof magnetic contamination.

References

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[13] Physics toolbox magnetome-ter. https://play.google.com/store/apps/details?id=com.chrystianvieyra.android.physicstoolboxmagnetometer. LastAccessed: 21.11.2018.

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