Ad ances in Elec ical and Elec onic Enginee ing
326
VISUALISATION OF MAGNETIC FIELDS GENERATED
BY HELMHOLTZ COILS
J. Šu iansky, T. F ank
Depa men o In o ma ics and Au oma ion Technologies, Technical Uni e si y Z olen,
T. G. Masa yka 24, 960 53 Z olen, Slo ak Republic,
e-mail: su ian@ sld. uz o.sk, ank@ sld. uz o.sk
Summa y This a icle deals wi h a me hod o a homogenous magne ic ield gene a ion using Helmhol z coils.
The e is also an expe imen o a magne ic ield isualisa ion wi h a digi al image p ocessing pe o med wi h a
magne o- esis i e senso desc ibed. A he end o his a icle, he e is a possibili y o pe meabili y measu emen
using digi al images o a magne ic ield shown.
Key wo ds: homogenous magne ic ield, digi al image, senso
1. INTRODUCTION
We can ully desc ibe an elec omagne ic ield
wi h hese ou ec o unc ions o posi ion: elec ic
in ensi y E [V.m
-1
], elec ic induc ion D [As.m
-2
],
magne ic in ensi y H [A.m
-1
] and magne ic induc ion
B [Vs.m
-1
].
To de ine an elec omagne ic ield in a speci ic
a ea means o de e mine hese ou ec o s o
elec omagne ic ield in each poin o his a ea.
I is possible o depic a homogenous magne ic
ield wi h i on chips when we pu hem in o a
magne ic ield. I he chips a e in pa allel lines and
hese lines a e in equal dis ances, he ield in his
a ea is homogenous. The densi y o chip lines gi es
he ampli ude o magne ic induc ion B. The highe
densi y means highe ampli ude o magne ic
induc ion.
Nowadays, i is possible o depic a magne ic
ield wi h digi al image using senso s o magne ic
ield.
2. GENERATION OF MAGNETIC FIELD
USING HELMHOLTZ COILS
Helmhol z coils (Fig. 1) a e wo iden ical hick
ci cula coils wi h N cu es and he same cu en I
placed in he dis ance 2m ha is equal o hei adius
ρ
0
.
2
0
ρ
=m
(1)
The in ensi y o he magne ic ield o wo
iden ical coils wi h adius
ρ
0
coaxially placed on Z-
axis, which cen es a e in he poin s (0, 0, +m) and
(0, 0, -m), is he supe posi ion o ec o s H
1
and H
2
de e mined by equa ions o he ampli ude o ec o
o magne ic in ensi y H on Z-axis (2).
[ ]
Z
u
Z
IN
ZH ..
2
.
),0,0(
2
3
2
0
2
2
0
ρ
ρ
+
=
(2)
( )
[ ]
z
u
mZ
IN
ZH ..
2
.
),0,0(
2
3
2
0
2
2
0
1
ρ
ρ
+−
=
(3)
( )
[ ]
z
u
mZ
IN
ZH ..
2
.
),0,0(
2
3
2
0
2
2
0
2
ρ
ρ
++
=
(4)
),0,0(),0,0(),0,0(
21
ZHZHZH +=
(5)
The coils a e in e connec ed in he way ha
makes he cu en s in hem o ien a e in he same
di ec ion so he ampli ude o esul an ec o is
de e mined by equa ion (5). I we pu he equa ions
(1), (3) and (4) in o he equa ion (5), we will ob ain
he inal equa ion (6).
z
u
ZZ
NI
ZH
+
+
+
+
−
=
2
3
2
0
2
0
2
3
2
0
2
0
2
0
2
1
2
1
2
),0,0(
ρ
ρ
ρ
ρ
ρ
(6)
Helmhol z coils a e used always when we need
o c ea e a homogenous magne ic ield in a de ined
a ea. Fig. 2 shows he dis ibu ion o magne ic
in ensi y o magne ic ield along he axis o hese
coils. We can see ha in he middle be ween he
coils he in ensi y changes i s alue only a li le and
Fig. 1.: Helmhol z coils
Visualisa ion o magne ic ields gene a ed by Helmhol z coils
327
i is nea ly independen on he posi ion on Z-axis. I
is easy o de e mine ha he in ensi y o magne ic
ield in poin s (0, 0, -m) and (0, 0, +m) is only
5.38% lowe han in he poin (0, 0, 0).
I he cu en h ough Helmhol z coils is
ha monic, he magne ic ield gene a ed by hese
coils is ha monic. In ha case he equa ions (2) and
(6) can be ans o med in o egua ions (7) and (8).
[ ]
z
m
m
u
Z
NI
ZH
2
3
2
0
2
2
0
2
),0,0(
ρ
ρ
+
=
(7)
z
m
m
u
ZZ
NI
ZH
+
+
+
+
−
=
2
3
2
0
2
0
2
3
2
0
2
0
2
0
2
1
2
1
2
),0,0(
ρ
ρ
ρ
ρ
ρ
(8)
The physical quan i y H
m
is he ampli ude o
ec o o magne ic ield in ensi y along he Z-axis
and I
m
is he ampli ude o cu en h ough he coils.
I is ob ious ha he dis ibu ion o al e na e ield is
he same as he dis ibu ion o di ec ield.
3. EXPERIMENT AND ITS RESULTS
A i s we designed and c ea ed he Helmhol z
coils and a e wa ds we measu ed he homogenei y
o magne ic ield in wo ways. We used wo
di e en alues o ampli ica ion o ampli ie
AMP04, which is a pa o magne o- esis i e senso
HMC1001.
The alue o ampli ica ion is o his ampli ie
de ined as in (9).
Rg
k
A
Ω
=100
(9)
In he i s case we used he alue o esis o
R
g
= 22
Ω
ha de e mined he alue o ampli ica ion
A = 4545.45. The exci a ion o Helmhol z coils was
se on he alues U = 1.1V and I = 0.08A. In ha
case he sensi i i y o he senso was 3.2mV/gauss.
The dis ibu ion o magne ic ield is shown in he
ig. 3.
Measu ed alues o magne ic ield show
di e ences in each pa icula poin o explo ed a ea.
The shape o magne ic ield o he Ea h causes
hese esul s.
In he second case we used he alue o esis o
R
g
= 100
Ω
ha de e mined he alue o
ampli ica ion A = 1000. The exci a ion o Helmhol z
coils emained he same wi h he alues U = 1.1V
and I = 0.08A. In ha case he sensi i i y o he
senso was 0.704mV/gauss. The dis ibu ion o
magne ic ield is shown in he ig. 4.
Du ing he nex measu emen we pu a piece o
pa amagne ic ma e ial (aluminium) wi h ci cula
c oss-sec ion in o he homogenous magne ic ield
( ig. 5). Aluminium is a pa amagne ic ma e ial ha
means ha he ec o o magne ic induc ion is
ampli ied only a li le. So he senso was se o he
highe sensi i i y. We used he esis o R
g
= 6.3
Ω
ha ma ch he alue o ampli ica ion A = 15873 and
he exci a ion o Helmhol z coils was se o he
Fig. 2.: Dis ibu ion o magne ic in ensi y o
magne ic ield along he axis o Helmhol z coils
Fig.3.: The shape o magne ic ield gene a ed by
Helmhol z coils wi h he ampli ica ion se on 4545
Fig.4.: The shape o magne ic ield gene a ed by
Helmhol z coils wi h he ampli ica ion se on 1000
Ad ances in Elec ical and Elec onic Enginee ing
328
alues U = 1.1V and I = 0.08A. The measu ed
dis ibu ion o magne ic ield is shown in he ig. 6.
Du ing he ou h measu emen we pu wo
pieces o e omagne ic ma e ial wi h ci cula c oss-
sec ion in o he homogenous magne ic ield ( ig. 7).
This kind o ma e ial ampli ies he ec o o
magne ic induc ion a lo , so we se he sensi i i y o
he senso o a lowe le el. The alue o
ampli ica ion was se o A = 1000 and he exci a ion
o Helmhol z coils was se o he alues U = 0.8V
and I = 0.05A. The measu ed dis ibu ion o
magne ic ield is shown in he ig. 8.
4. CONCLUSION
This expe imen is only he i s s ep in ou
de elopmen o a de ice ha will make possible o
measu e he pa ame e s o elec omagne ic ield in
he h ee dimensional space.
The esul o his expe imen is ha i is possible
o de e mine he pe meabili y o ma e ials using
me hods o digi al image p ocessing and analysis o
digi al image o magne ic ield.
The de eloped sys em is capable o measu e big
and also small changes o pa ame e s o magne ic
ield depending on he sensi i i y o senso ha can
be se by he ampli ica ion o ampli ie AMP04.
I is also possible o examine pa amagne ic
ma e ials ha a ec he magne ic ield only a li le.
Fig. 6.: The dis ibu ion o magne ic ield wi h
pa amagne ic ma e ial inside
Fig. 5.: Aluminium ma e ial in he homogenous
magne ic ield
Fig. 8.: The dis ibu ion o magne ic ield wi h
e omagne ic ma e ial inside
Fig. 7.: Fe omagne ic ma e ial in he homogenous
magne ic ield
Visualisa ion o magne ic ields gene a ed by Helmhol z coils
329
Bu he sys em is no app op ia e o diamagne ic
ma e ials.
This p oblem has been inancially suppo ed
and sol ed as a pa o he scien i ic p ojec VEGA
1/2172/05 Resea ch o Ma e ial P ope ies Using an
Analysis o Elec omagne ic Field De o ma ion.
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[3] DEDEK, L., DEDKOVÁ, J.: Elek o-
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[4] NEVESELÝ, M., ŠURIANSKY, J.: Teo e ická
elek o echnika, Vojenská akadémia
Lip o skom Mikuláši, 1998, ISBN 80–8040–
064–4
[5] TRIPÁK, A.: Elek ina a magne izmus II,
Uni e zi a Komenského B a isla a, 1997, ISBN
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[6] ŠURIANSKY, J., SABO, A.: Magne ic Field
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P ocessing. In: Radioelek onika 99 p. 462 –
465, 1999.
