magnetic field and its experimental measurement in teaching in … · 2016-04-28 · european...

European International Journal of Science and Technology ISSN: 2304-9693 www.eijst.org.uk

116

Magnetic field and its experimental measurement in teaching in high schools

Jozef Beňuška The Comphehensive School of Viliam Pauliny-Toth in Martin

Malá Hora 3, 03601 Martin, Slovakia

Daniel Polčin Department of Informatics

Faculty of Education, Catholic University in Ruzomberok Hrabovska 1,034 01 Ruzomberok, Slovakia

* Corresponding Authors

PaedDr. Beňuška Joseph, PhD.

E-mail: [email protected] RNDr. Daniel Polčin, PhD.

E-mail: [email protected]

Abstract:

The article demonstrates the possibilitiesof experimental measurement of magnetic field byhigh school

students.It refers to the possibility of using the investigative character of experiments, developing the

competencies that students need to understand the scope, meaning and methods of scientific work in the

proces of understanding natural phenomena and their laws.

The first part is focused on investigaive experiments with permanent magnets, through which students

actively, independently and creatively come to mathematical regularities verified by laboratory

measurements and observations in accordance with the theory learned in physics lessons.

The second part presents possibilities of experimental measurements of magnetic induction of the

geomagnetic field in the context of teaching physics in high schools. There are described two methods, by

which students independently, with their own creative approach and adjusting the experimental conditions,

using simple devices,individually measure the geomagnetic field on their latitude and compare their

measurements with tabulated values.

Keywords: investigative experiment, magnetic field, charge, magnetic induction, measurement, magnets, measuring instruments

European International Journal of Science and Technology Vol. 5 No. 3 April, 2016

117

Investigative experiments with magnets

Students at a high school have a certain amount of science knowledge. However, if they are to form hypotheses based on the studied scientific problems or interpret the observed facts, they find it difficult. Students should understand the meaning, purpose and methods of scientific work onexamples of knowing of natural objects, phenomena and laws (Mazurová-Slabeycius, 1995).

The article brings some inspiration for creating the conditions for an investigative method of teaching physics in high schools. The key principles of inquiry-based teaching and learning: 1. Students are, in the process of learning,lead by questions, problems to be answered (why ?, how?). 2. Students look for empirical evidence as a basis for their explanations of answers to the questions and

problems (data collection of observations and measurements). 3. Students formulate explanations based on empirical evidence. 4. Students evaluate their explanations in the face of alternative explanations (discussion to the results,

comparison of the results etc.). 5. Students share and defend their explanations.

The inquiry activities may vary depending on the degree of involvement of a student, a teacher respectively, as well as on a support by learning materials. For so called bound research it is true that students receive a problem formulated by teachers (Kíreš, 2007) and:

• they design and implement an experiment alone with little or no support from a teacher, • the activity is difficult to implement, students must already have sufficient experience of an

implementation of previous types of activities. The following are a few ideas for a bound research for students at high schools.

1. A problem of dependence of the size of magnetic forces acting between two magnets on their

mutual distance. The size of gravitational forcesacting between two bodies and of electrostatic forces acting between two

point charges will vary depending on the distance of bodies,between which these forces act.

Figure 1: Mutual gravitational and electrostatic force action

From Newton's law of gravitation and Coulomb's law of the described dependence it follows that if at a

distance r the size of the forces is F, then at a distance 2r the size of forces drops to F/4. In terms of a quantity equation the relation can be written as

r

gF g- F

2gr

kF =

2er

kF =

r

eF e- F

eFe- F


In the constant k there are also expressed the characteristics of objects - their weight and electrical charge. Mutual force interaction also exists between the two poles of permanent magnets. In this case it can be

relatively easy to manually identify that the size of magnetic forces, by which with the magnets interact, varies with the distance.

On the basis of the above-described dependence for the gravitational and electrostatic forces, students can be introduced into the problem they are to solve, namely: is there, for the size of magnetic forces acting between the magnet poles, the same dependence on the distance as in the case of gravitational and electrostatic forces?

Figure 2: Mutual force interaction between two magnets

If into a suitable measuring cylinder two magnets are inserted so as to be rotated to each other with

concordant poles, one magnet will drop to the bottom of the measuring cylinder and the other will remain above it at a certain height and will levitate. In this position, there will be a steady state, on the upper magnet there acts repulsive magnetic force F m and it is as big as the gravitational force F G, acting on it.

To this state there corresponds a certain distance of magnets r(see the Figureure). Figure 3: Sizing of magnetic force acting between two magnets

If the upper magnet is loaded with a known weight, the magnets get closer to each other but again at a

certain distance there will be a steady state and the upper magnet will levitate. In this state,the magnetic force F m is equal to the sum of the gravitational force F G1, acting on the weight, and the gravitational force F G, acting on the magnet.

2r

kF =

?2m

r

kF =

r

mF m- F

m- F mF

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European International Journal of Scien

To this state there corresponds the dis

Figure 4: Sizing of the magnetic forc

magnets

With another change of theweight itis po Table 1: Measured values

No. m. m / 10 -3 kg F

1 6 0.

2 16 0.

3 26 0.

4 36 0.

5 46 0.

6 56 0.

Using Microsoft Excel, the measureddistance of magnets - see the graph. Figure 5: Graph of the size dependenc

m

10−2N

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distance of the magnets r 1 (see the Figureure).

rce acting between two magnets in changing

possible to measure the dependence of F m = f (r).

G = F m / N r / 10 -3 m

0.06 49

0.16 38

0.26 34

0.36 31

0.46 29

0.56 27

ed values can be displayed as a plot of magnetic fo

nce of magnetic forces from a distance of magn

10−2m

April, 2016

g the distance of the

r).

force from the mutual

gnets poles

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Using the tools of Microsoft Excel: will be an equation that describes the plo in which as an exponent at x, which is ou

The experiment concludes that the s

our experiment act on each other, varies If students at the beginning faced the

magnetic forces acting between the mforces, the results of measuring do not sdependence is correct? First, a bit of theo

Magnetic dipole is a body which pelectric dipole. As a dipole there can besouth magnetic poles, hence the name di

Figure 6: Magnetic and electric dipole

Magnetic dipole is characterized by aAnalogously,electric dipole is charactElectric dipole moment is a vector q

usually of a molecule or a small group ofIn the most simple case, when tw

distance d, the size of the dipole momenjunction of point charges.

Figure 7: Electric dipole moment

=y

mF =

+Q -Q

d

p

ence and Technology ISSN: 2304-9693

: Format trendline - Options of trendline - Gra

lot

our r, there is a number 3,812.

size of the magnetic forces, by which the two mies with the distance of the magnets.

he problem, if the same dependence on the distancmagnet polesas well as inthecase of gravitationt support the hypothesis. How to persuade studeneory is needed. produces around itself a magnetic field similabe also understood a conventional permanent ma

dipole.

le

a vector quantity - the magnetic dipole moment mcterized by a vector quantity-electric dipole momr quantity describing the unbalanced distribution of atoms. two point charges of opposite sign + Q and

ent of the pair of charges is p = Qd, the direction

812,372 −+ xE

48,3r

k

r

k≅=

www.eijst.org.uk

raphed equation, there

magnets described in

ance also applies to the ional and electrostatic

nts that the measured

ilar to the field of an magnet with north and

m. ment p. n of electrical charge,

-Q are located at a n of vectors lies at the

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Magnetic dipole moment is a vectomoment is a fundamental elementary particles, atoms, magnetized

Magnetic dipole is similar to an elecof poles of a magnetic field source.

Such an idealized model can be imelementary particles, carriers of opposiconventional, since the existence of a ma

Figure 8: Magnetic dipole moment of

As well as an electric dipole, a ma

material bodies interiors. The primary pdipole because each electron "orbiting" a

A free dipole placed in an external mamoment to have the same direction as th

Thus, e.g. magnetsplaced loose on a topposite poles towards each other. For tdirection of magnetic induction lines. Atenergy.

Let us return to our experiment and itAt the experiment we used two cylinparameters: Height h(mm): 10 Diameter d (mm): 10 Finish: nickel Weight: 6 g Temperature resistance: 80 °C Magnetic force (N): 39

The magnetsheight h is comparable toproblem of how the size of the magnetic

ence and Technology Vol. 5 No. 3

ctor quantity describing the sources of the magl quantity describing the magne

ed objects, but also of closed conductors (coils) wiectric dipole. It is defined for limited and closed c

imagined as a system of two "magnetic monoposite magnetic charges (similar to electrical charmagnetic monopolehas not been experimentally pr

f a current loop and two magnetic "hypothetic

magnetic dipole also has practical significance particle of a structure of any matter–an atom - i" around the core actually createsa perfect current magnetic field will rotate influenced by a magnetithe magnetic induction of the field. a table near to each other will orientate approvingl

the same reason, iron filings around a magnet wAt the approving orientation a dipole has namely t

its explanation. lindrical magnets, magnetized axially - parall

to the distance between the nearer poles of magntic forces changeswith a mutual convergence of m

April, 2016

agnetic field. Magnetic netic properties of with electric currents.

current loop or a pair

opoles" - hypothetical arge). This analogy is proven.

tical" monopoles

e for a description of is always a magnetic

nt loop. etic force for the dipole

gly, which means with will be oriented in the the smallest potential

allel to the axis with

gnets r. We solved the magnets.

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Figure 9: Model of experiment

Based on the analogy with the electrical charge, we can illustrate the force action between magnetic

dipolesby an alternative view, where the mutual force action between the poles of the magnets is replaced by electrostatic forces between charged bodies. Then there exists a mutual force action among all the poles. In the graph we can illustrate the acting forces as in Figure 10.

Figure 10: The resulting force acting between the dipole is given by the vector sum of the forces acting

between the individual poles of dipoles

For the size of the forces acting between the different poles of dipoles itis valid: The resulting force is given by the vector sum of all the forces and therefore:

Substituting: After adjusting to a common denominator for the resulting force, the relation is:

r

h

mF

mF-

r

h

r

h 1F

1F-

r

+ + +

+ + +

F

F-

2F

2F-

r

h 3F

3F-

+ + +

- - -

+ + +

- - -

- - -

- - -

+ + +

- - -

21r

kF =

( )222hr

kF

+=

( )23hr

kF

+=

321m 2FFFF −+=

( ) ( )222m 22 hr

k

hr

k

r

kF

+−

++=


Considering the analogy to an electrical charge, the constant k is:

When we substitute, we get out of the part while is by definition equal to the size of the dipole moment. In the case of a magnetic dipole, the quantity is the magnetic dipole moment (Q m is a hypothetical magnetic charge with the same qualitative characteristics as an electric charge –the magnetic field lines around it are formed as with the electric charges creating an electric field). The magnetic force will then be

For a very small h is then which is fine as it is in accordance with the measurements.

The force action of the magnetic dipole on the next dipole in a relative position, which was used in the experiment, decreases with distance as 1/r4,as also confirmed by the experiment. The described proposal of the investigative activity:

• fulfills the key principles of a inquiry-based learning, • corresponds with the aims of theState Educational Program of the Slovak Republic, • shows a fine agreement between an experimental detection and a theory.

1. If you would like to continue in this experiment with students,itis possible so that you will study

the same dependence at the position of magnets, in which only the same poles of magnets will repel - see Figure 11.

Figure 11: The interaction between magnetic dipoles at a different position of dipoles

( )( ) ( )222

222

m2

2632

hrhrr

hrhrkhF

++

++=

0

2

4πε

Qk =

222hQkh ≈

Qhd =

hQm m=

( )( ) ( )222

222

m2

2632

hrhrr

hrhrmF

++

++=

4

2

mr

mF ≈

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The magnets suitable for this experimeto the axis,e.g. http://e-shop.magsy.cz/ne

Figure 12: Magnet magnetized perpen

Geomagnetic field

The geomagnetic field,or also the Eamanifested by magnetic forces. It extendan important protective factor for the bio

The magnetosphere does not allowsurface. The charged particles are forthe terrestrial poles there is in the magnecharged particles may enter the deepermove in two areas known asVan Allen ra

The magnetic field thus fulfills a propossible.

The Earth is one of the two solid planto which the Earth's magnetic field is mother minor bodies of the solar system wind.

Figure 13: The Earth's magnetic field

A Measurement of the horizontal com

by a threadrotation The experiment is designed to measu

latitude by means of a rotating condwithFaraday's law of electromagnetic incircumscribed by the conductor.1

1Horváth, P: Meranie indukcie MP Zeme na strehttp://www.slideserve.com/dyami/meranie-induk

ence and Technology ISSN: 2304-9693

ent are cylindrical neodymium magnets magnetneodymove-magnety-valce-kolmo-na-osu.

endicularly to the axis.

Earth's magnetosphere, is in the space around thends up from many thousands to one hundred thouiosphere.

ow electrically charged solar wind particles torced during their motion to follow magneticnetosphere a so calledpolar peak, an unstable areer layers of the Earth's magnetosphere. The cap radiation belts. rotective function, without which the life on the

lanets that have their own magnetism. The other ismuch stronger. All gas planets also have their o

m have only an induced magnetism, exerted by t

omponent of the magnetic induction of the Ea

sure the size of the magnetic induction of the geoductor, in which on rotation a voltage is indinduction at the change of magnetic induction f

rednej škole. ukcie-mp-zeme-na-strednej-kole

www.eijst.org.uk

etized perpendicularly

he Earth, in which it is ousand kilometers. It is

to reach the Earth's tic field lines. Above

area through which the captured particles then

he Earth would not be

is Mercury, compared r own magnetic fields, y the magnetized solar

Earth´smagnetic field

eomagnetic field in our nduced in accordance

flux through the area

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In our latitude (Slovakia, Ruzomberok: GPS N49,082647 - E19,293574) the magnetic induction is B = about 5 x 10 -5 T, of which the horizontal component B h = 2 x 10 -5 T. Tools:

a solid wire (20 m) loaded in the middle by a tennis ball, millivoltmeter, stopwatch, lenght meter, compass to determine the correct direction –the flat of thread surface must be perpendicular to the direction south-north.

Figure 14: Ready devices, taking of measurements

Measurement procedure

In the Earth, we are in its magnetic field. In accordance with Faraday's law of electromagnetic induction, when there is a time change of the

magnetic induction flux Φ in a thread, it induces the voltage U.

When we spin the conductor in the magnetic field of the Earth in the direction south-north, we constantly

change during spinning the surface of the thread, through which the magnetic induction lines run. Thus we change the magnetic inductive flux and there is a voltage induced in the thread.

By a millivoltmeter we can measure the size of the induced voltage and from this value calculate the size of the magnetic induction of the geomagnetic field. The size of the induced voltage can be expressed by a relationship

Figure 15: The scheme of experiment

t

ΦU

∆

∆−=

.∆

∆.

t

SBU =

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European International Journal of Science and Technology ISSN: 2304-9693 www.eijst.org.uk A maximum change of the surface is 2S∆ This change will occur in a half of the period

The magnetic induction MP of the Earth has thus the value where U is the induced voltage (an effective value),

T is a period ofthreadrotation,

S∆ isa content of the surface ofdescribed triangle.

Figure 16: The measurement of surface of the described triangle

Figure 17: The measurement of induced voltage at the thread rotation

.

2

2T

SBU ∆=

,4 ∆

=S

UTB

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Figure 18: The evaluation of measured results

Table 2: The measured values

no. m. 10 T / s T / S U / mV

1 10.81 1,081 0.31

2 11.57 1,157 0.30

3 10.36 1,036 0.40

4 11.57 1,157 0.29

5 11.59 1,159 0.28

Average values: U = 0.32 mV, T = 1.118 s.

Triangle surface: S ∆ = 4.07 m2 The size of measured horizontal component of the magnetic induction of geomagnetic fieldB h = 2.27 x 10 -5 T.

B Measurement of the horizontal component of the magnetic induction of the geomagnetic field, using

a circular coil Tools:

a circular coil (31 threads, diameter 20 cm), paper box, compass (magnetic compass), U e =4.5 V voltage supply (battery), 100 Ω potentiometer, ampermeter (up to 300 mA).

Measurement procedure The principle consists in comparing the size of the magnetic induction of the magnetic field created by the electric current in the coil and the size of the horizontal component of geomagnetic field.

European International Journal of Science and Technology ISSN: 2304-9693 www.eijst.org.uk Figure 19: The influence of coil magnetic field and geomagnetic field on a magnetic needle

When set by electric current α = 45 °, we get the equality B = B Z.

Where µ permeability of the medium (for air appriximately as for vacuum 4π x 10 -7 N x A-2), N number of threads in a circular coil, I current through the coil threads, d coil diameter.

Figure 20: The scheme of connections

Figure 21: Ready tools

zB

CB

Bα

Z

C

B

B=αtg

d

NIBC µ=

eU

A Ω 100

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Figure 22: The circuit with a circular coil – magnetic needle points north

Figure 23: The rotation of magnetic needle by the a coil magnetic field by 45°

Figure 24: The processing of measured results

From the measured values of quantities N = 31, I = 98.4 mA = 0.0984 A and d = 20 cm = 0.2 m, the size

of horizontal component of the magnetic induction of geomagnetic field

Bh = 1,91 x 10 -5

T.

The result of the first measurement method could be specified by measuring the voltage induced at a

more constant thread rotation, which the students at our measurements did not manage to ensure completely. The result of the second methodcould be specified by measuring the electric current in a precise

deflection of a magnetic needle at an angle of 45°, which unfortunately fluctuated slightly due to instability

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of the assembled circuit. The movement and deflection of magneticneedle were also affected negatively during measurementbythe magnetic fields of reproduction speaker system at the computer laboratory, which we noticed as late as at the analysis of measurement results and their interpretation.

In the both methods of measurement, whatwe mainly consider valuable and vital is the obtained experimental experience of the students, which positively exceeds the accuracy of measurement results.

Conclusion

A practical verification of acquired physical knowledge in laboratory exercises is a very important, integral part of teaching physics at all levels of education. It brings students to individual creative investigative work, but also to a collective preparation, implementation and interpretation of measurement results.

Students acquire competencies necessary for a scientific approach to science education, a critical view on the interpreted content of the curriculum in physics and build a positive attitude towards science and technology disciplines, in the spirit of the needs of contemporary science and technology (Klieger - Sherman, 2015).

Literature HORVÁTH, P. 2012:Measurement of geomagnetic field induction in a high school.

http://www.slideserve.com/dyami/meranie-indukcie-mp-zeme-na-strednej-kole KÍREŠ, M. 2007.Archimedes' principle in action.Physics Education 42(2007), N 5, 484-487. ISSN: 1361-6552 KLIEGER, A- SHERMAN, G 2015.Physics textbooks: do they promote or inhibit students' creative

thinking.Physics Education 50 (2015), N 3, 305-309. ISSN: 1361-6552 LINN, M.C.- DAVIS, E., A.- EYLON, B., S. 2004.The scaffolded knowledge integration framework for

instruction.In: Linn, M.C., David, E.A., Bell, P.: Internet environments for science education, 2004, Lawrence Erlbaum Associates: Mahwah, NJ, 47‐72

MAZUROVÁ,J.-SLABEYCIUS,J. 1995.Newspaper articles and physics teaching. Physics Education 30 (1995), 297-301.ISSN: 1361-6552

Project ESTABLISH, available at <www.establish‐fp7.eu> http://en.wikipedia.org/wiki/Dipole_model_of_the_Earth%27s_magnetic_field http://www.ddp.fmph.uniba.sk/~koubek/UT_html/G3/kap1/1-1.htm

magnetic field and its experimental measurement in teaching in … · 2016-04-28 · european...

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