Observation of magnetic field lines in the vicinity of a superconductor
with the naked eye∗
Yoshihiko Saito

Osaka Science Museum, Osaka-shi 530-0005 Japan†
Meissner effect and pinning effect are clearly observed with the naked eye. A GdBaCuO hightemperature superconductor (HTS) disk fabricated by Nippon Steel Corporation, a 100mm cubic
NdFeB sintered magnet, and iron wires coated by colored vinyl are used. When the HTS is put inthe magnetic field of the magnet, it can be observed by the wires that the magnetic field lines are
excluded from the superconductor (Meissner effect) as well as are pinned in the superconductor(pinning effect).
PACS numbers: 01.50.My

I.

INTRODUCTION

A demonstration of superconductivity with a hightemperature superconductor (HTS) was demonstrated as
early as the year of the HTS discovery [1]. Soon, apparatuses for the demonstration were developed[2], [3],and rigid levitation and suspension of the HTSs by magnets were discussed taking account of pinning effect[4].
Today, even beginners can enjoy large-scale phenomena of superconductivity and have strong impression.
For example, Fig. 1 and Fig. 2 are the demonstrations
with a GdBaCuO HTS disk fabricated by Nippon SteelCorporation[5]. The disk size is diameter 60mm andheight 10mm. In Fig. 1, a NdFeB sintered ring magnet
is repelled by the HTS and the horizontal movements ofthe magnet are restricted by a pair of chopsticks, so themagnet is floating above the HTS. Fig. 2 is a continuous
shot, namely, (a) suspended HTS, and (b) (c) capsizedmagnet with the HTS. It can be seen that the relative
position of the HTS and the magnet is kept at a fixed
distance. If these two phenomena are shown successively,
the demonstration will be more magical and more mysterious, because they are interactions of the same HTS andthe same magnet. However, no one could see the essenceof superconductivity.
There are two basic types of superconductors, Type 1
and Type 2[6]. In the case of Type 1, there is a criticalmagnetic field Hc . If the external magnetic field strengthis less than Hc , the superconductor is in superconducting
state and the magnetic field lines are excluded from thesuperconductor. This phenomenon is called the Meissner effect[7]. Meissner effect as well as zero electricalresistance is one of the elementary properties of superconductivity. If the external magnetic field strength isgreater than Hc , the superconductor is in normal state.
In the case of Type 2, there are two critical magnetic
fields, Hc1 and Hc2 (Hc1 < Hc2 ). If the external magnetic field strength is less than Hc1 , the superconduc-∗ This preprint will be submitted to American Journal of Physics.
† Electronic address: saito[atmark]sci-museum.jp

tor is in superconducting state. If the external magnetic
field strength is greater than Hc2 , the superconductor isin normal state. If the external magnetic field strength
is between Hc1 and Hc2 , a part of the external magnetic field flux penetrate the superconductor and otherpart is excluded from it. Microscopically, the quantized
fluxes with normal state core, called vortex, penetrate
the superconductor and the vortex lattice is formed by
the interactions between the vortexes[8], [9]. The outsideof these normal state cores is in superconducting state.
This coexisence of the normal state and the superconducting state is called mixed state. In the case of Type1, the mixed state is forbidden. All known HTSs are in
Type 2.
The phenomenon that a magnet floats above a HTS(Fig. 1) is caused by Meissner effect. In the HTS, themagnetic field of the magnet is canceled by induced supercurrents and mirror images of each pole are produced;
therefore, the magnet is repelled by the HTS. The phenomenon that a HTS is bound to a magnet at a fixed distance (Fig. 2) is caused by pinning effect and the Meissner
effect[4], [10], [11]. The pinning effect is the phenomenon
that a vortex lattice is pinned by the defects in the superconductor crystal. At the macroscopic level, the pinningeffect is the phenomenon that the magnetic field lines
cannot move and change inside a superconductor. In
Fig. 2, while the Meissner effect acts repulsively, the interaction between the magnet and magnetic poles for themagnetic field lines pinned in the HTS acts attractively,
therefore, the HTS and the magnet do not get too close
as well as too far each other.
If the demonstration is scientific one but not an astonishment show, the behavior of the magnetic field lines
should be mentioned and it is desirable that the magnetic
field lines are visualized.
Though quantitative considerations had been
made[4], [10], [11], no one seems to know a demonstration such that the beginners observe the magnetic
field lines in the phenomena. There are explanations of
the phenomena with some illustrations or animations,but unfortunately it may be difficult for the beginners
to accept them, because they are unrealistic. Therefore,
it is desirable that the beginners observe the magnetic

the pinning effect will be shown.

II.
FIG. 1: Mmagnet floating above a superconductor. A HTS
is cooled in liquid nitrogen. A NdFeB sintered ring magnet isrepelled by the HTS. The horizontal movement of the magnet
is restricted by a pair of chopsticks.

(a)

(b)

VISUALIZATION OF MAGNETISM IN
SUPERCONDUCTIVITY

In this section, we will observe the magnetic field lines
in the vicinity of the same HTS in Fig. 1 and Fig. 2. The
HTS will be put in the magnetic field which is caused bya 100mm cubic NdFeB sintered magnet of magnetic flux
density about 0.5T at the surface (Fig. 3). The magnetic
field is shown by iron wires that are coated by coloredvinyl to observe more clearly. In Fig. 3, the wires in theacrylic cases stand against the force of gravity under the
influences of the magnetic field, though the wires lie flatoutside of the magnetic field. The wires are almost free tomove and rotate under the influences of the magnetic fieldand gravity with some friction between the wires and theacrylic cases. The direction any wire points is tangent tothe curve of a magnetic field line and the density of thewires corresponds to that of the magnetic field lines, themagnetic flux. Given some vibration to the acrylic cases,
the density is close to the ideal one and the effect of thefriction becames negligible. The principle of this method
is the same as that of the well-known observation withiron filings. The effect of gravity on the wires is negligiblefor qualitative understandings unless we observe too far
from the magnet. They are enough to supply qualitative
information. The magnetic field lines for the Meissner
effect as well as for the pinning effect are observed asfollows.

(c)

FIG. 2: Superconductor bound by a magnet at a fixed distance. (a) A HTS is suspended by an NdFeB sintered ringmagnet (the held black object). (b) (c) The magnet is capsized. The relative position of the HTS and the magnet is
kept at a fixed distance.

field lines with the naked eye.
In 1989, A. Tonomura et al. visualized the magnetic
field lines in superconductivity at the vortex level by theuse of electron holography and digital phase analysis[8].
This is a historic observation for basic research as well as
for industrial applications. For the beginners, however,this method is too complicated to use or understand.
The author developed a very simple observation oflarge-scale magnetic field lines with the naked eye, andvisualized the Meissner effect[12]. For the case of thepinning effect, he did not observe the magnetic field lines
pinned in a HTS. The observation of the pinning effectwas not complete. In this article, observations of themagnetic field lines for the Meissner effect as well as for

FIG. 3: Magnetic field lines diverging from a 100mm cubic
NdFeB sintered magnet of magnetic flux density about 0.5T
at the surface. The magnetic field lines are shown by the iron
wires in the acrylic cases.

(a)

(a)

(b)

FIG. 4: Meissner effect shown by wires. The wires are: (a)on a transparent plastic board on the top of the HTS; (b) in
the transparent plastic cases divided by multistage on the top
and the bottom of the HTS. There exists the 100mm cubic
NdFeB sintered magnet below the HTS and the HTS is in theexternal magnetic field caused by the magnet. There is nowire on the HTS, while the magnetic field lines in the vicinityof the HTS are shown by the wires. It can be seen that theexternal magnetic field liens are excluded from the HTS.

A.

The Meissner effect

In this section, we use the HTS cooled by the following
method. The HTS is put in near zero external magnetic
field while the HTS is cooled in liquid nitrogen, i.e., at thetransition from the normal state to the superconducting
state. The HTS in Fig. 1 has been cooled by this method.
In both figures of Fig. 4, the HTS is put above the100mm cubic NdFeB sintered magnet, i.e., in the external
magnetic field caused by the magnet. In Fig. 4(a), there
are the wires on a transparent plastic board on the topof the HTS. It is shown by the wires that the magnetic
field lines do not exist on the HTS. In Fig. 4(b), there
are the wires in the transparent plastic cases divided bymultistage on the top and the bottom of the HTS. It
is shown by the wires that the magnetic field lines do
not penetrate the HTS. It can be seen that the external
magnetic field lines are excluded from the HTS like Fig. 5.
This is the very Meissner effect.

B.

The pinning effect

In this section, we use the HTS cooled by the following
method. The HTS is cooled below the NdFeB sinteredring magnet like Fig. 6. In other words, the magnetic
field lines of the magnet is penetrating at the transition
from the normal state to the superconducting state. The
HTS in Fig. 2 has been cooled by this method. If the
HTS is cooled to a temperature such that Hc2 is equal tothe magnetic field strength in the HTS, the HTS will bein the mixed state and the spatial distribution of mag-(b)FIG. 5: Diagram of the Meissner effect. (a) The free magnetic
field lines diverging from a magnet. (b) The magnetic fieldlines are excluded from the HTS(Meissner effect).

FIG. 6: A cooling method to cause Fig. 2. Before cooling,
the magnetic field lines of the magnet penetrate the HTS,
and after cooling, they are pinned in the HTS.

netic field will be macroscopically kept inside of the HTS
as well as outside without changing. Furthermore, if the
HTS is cooled to liquid nitrogen temperature, the distribution will be still kept without changing. The HTS will
be penetrated by the magnetic field lines in the same
distribution before the cooling. If the magnet is kept
away from the HTS, the distribution in the HTS will notchange. Microscopically, the distribution in the HTS willbe the vortex lattice and will be fixed by the deffects in
the HTS crystal even if the external magnetic field varies.
This is the pinning effect. The supercurrent around any
vortex responds to the variety of the external magnetic
field to keep the vortex. If there was no defect in the
HTS crystal, no vortex would be trapped in the HTS.
This cooling method is macroscopically like copying of
the magnetic field lines of the magnet into the HTS. If
the HTS was a Type 1 superconductor, the magnetic
field lines would be excluded from the HTS because thecoexisence of the normal state and the superconducting
state is forbidden in Type 1 superconductors. Though
all known HTSs are Type 2 superconductors, the mixed
state does not occuer when the magnet get close to the
HTS in Fig. 1, because the magnetic field strength at thesurface of the magnet is less than Hc1 at liquid nitrogentemperature.
In Fig. 7 and Fig. 8, the HTS is put above the 100mm
cubic NdFeB sintered magnet, i.e., in the external magnetic field caused by the magnet. There are the iron
wires on a transparent plastic board on the top of the
HTS. The magnetic field lines in the vicinity of the HTS

(a)

(b)

(a)

FIG. 7: Pinning effect against increasing external magnetic
field strength. The magnetic field lines diverging from NdFeB
sintered ring magnet are “copied” into the HTS. The HTS is
at a distance of (a)190mm, (b)60mm, from the 100mm cubic
NdFeB sintered magnet. There are the wires on a transparent
plastic board on the top of the HTS. It is shown by the wires
that the magnetic field lines penetrate a ring area in the HTS
and do not move in it for the change of the external magnetic
field strength.
(b)

are shown by the wires.
Fig . 9 is a diagram for Fig. 7. In Fig. 7(a), the HTS is
put at a distance of 190mm from the 100mm cubic NdFeB
sintered magnet and the magnetic field lines penetrating
the HTS are close near the HTS as shown by Fig. 9(a),because the external magnetic field is negligible for theflux of the penetrating magnetic field lines. In Fig. 7(b),the HTS is put at a distance of 60mm from the 100mm
cubic NdFeB sintered magnet. As shown by Fig. 9(c),some magnetic field lines diverging from the 100mm cubic
NdFeB sintered magnet are connected to the magnetic
field lines penetrating the HTS and the other magnetic
field lines avoid the HTS. It should be emphasized thatthe magnetic field lines penetrating the HTS are pinned
in HTS.
Fig . 10 is a diagram for Fig. 8. If the HTS is moved
in the horizontal direction, the magnetic field lines penetrating the HTS are pinned in the HTS, trailed by the
movement, and made longer. In Fig . 8(a) ( Fig . 8(c)),
a force to the right (left) direction is applied to the magnetic field lines in the HTS because tension occurs on thelonger magnetic field lines as shown by Fig . 10(a) (Fig
. 10(c)). It can be seen that the magnetic field lines are
pinned against the force. These are the very macroscopic
pinning effect.
It can be seen that the magnetic field lines penetrating
the HTS do not move in the HTS even if the external
magnetic field changes. Though it cannot observe thepinned vortex lattice by the method in this paper, Fig. 7
and Fig. 8 show the pinning effect macroscopically andthe “copied” magnetic field lines from the ring magnet.
Fig. 11 is the case that the HTS had been cooled below the NdFeB sintered columnar magnet like Fig. 6 anda rigid levitation of a NdFeB sintered columnar mag-(c)FIG. 8: Pinning effect against tension of external magnetic
field. The magnetic field lines diverging from NdFeB sinteredring magnet are “copied” inside the HTS. The HTS is moved
in the horizontal direction above the 100mm cubic NdFeB
sintered magnet, (a) on the upper right of, (b) just above,(c) on the upper left of, the magnet. There are wires on atransparent plastic board on the top of the HTS. It is shownby the wires that the magnetic field lines penetrate a ring areain the HTS and do not move in it against the tension of theexternal magnetic field.

net above a superconductor occurred. In Fig. 12(a),Fig. 12(b), and Fig. 12(c), the HTS is at a distanceof 190mm, 150mm, and100mm respectively from the
100mm cubic NdFeB sintered magnet. The flux of themagnetic field “copied” in the HTS is comparable tothat of the external magnetic field. It may be seen
more clearly than Fig. 7 that the magnetic field lines
do not move in the HTS even if the external magnetic

(a)

(a)

(b)

(b)

(c)

(c)

FIG. 9: Diagram of pinning effect against increasing external magnetic field. If the HTS penetrated by the magnetic
field lines is brought close to a magnet, the magnetic fieldlines penetrating the HTS will begin to be connected to those
diverging from the magnet. The magnetic field lines cannot
move in a HTS because of the pinning effect.

FIG. 10: Diagram of pinning effect against tension of external
magnetic field. If the HTS penetrated by the magnetic fieldlines is moved in the horizontal direction, the magnetic fieldlines pinned in the HTS are trailed and made longer. Forces
are applied to the magnetic field lines in the HTS to the left(a) or right (c) direction for the tension of the longer magnetic
field lines. However, the magnetic field lines cannot move inthe HTS because of the pinning effect.

field changes.
Movies show much more clearly than these figures[13].
These represent the pinning effect qualitatively.
C.

Superconducting state breaking

Fig. 13 represents a breaking superconducting state
when the HTS in Fig. 7 is warmed in the room temperature. Fig. 13(a) show the magnetic field lines “copied”
from the ring magnet into the top of the HTS. The area
where the magnetic field lines do not penetrate is in the

superconducting state. The area where the magnetic fieldlines penetrate is in the mixed state, that is, the vortex
lattice is formed in this area. In Fig. 13(b), on the one
hand, the superconducting state area seems to decrease,on the other, the mixed state area seems to increase. This
is why the critical field strengths Hc1 and Hc2 decrease
with the HTS temperature. To be exact, for the HTS
is inhomogeneously warmed, the superconducting statearea and the mixed state area are turning into the mixed
state area and the normal state area respectively. It can

FIG. 11: Rigid levitation of a NdFeB sintered columnar magnet above a superconductor.

(a)

(a)

(b)

(b)

(c)

(c)

FIG. 12: Pinned magnetic field lines of a NdFeB sinteredcolumnar magnet. The HTS is at a distance of (a)190mm,(b)150mm, (c)100mm, from the 100mm cubic NdFeB sinteredmagnet. There are wires on a transparent plastic board on
the top of the HTS. It is shwon that the magnetic field lines
penetrate a circle area in the HTS and do not move in it forthe change of the external magnetic field.

be seen at least that the area where the wires exist is in
the mixed state or the normal state. In Fig. 13(c), themagnetic field lines penetrate all over the HTS. If Hc2 isless than the external magnetic field strength in the whole
HTS, then the whole HTS is in the normal state. Thisphenomenon is the transition from the superconducting
state to the mixed state and from the mixed state to thenormal state. A movie shows this phenomenon of thesuperconducting state breaking much more vividly thanthese figures[13].
It may be useful for students to investigate mag-

FIG. 13: Superconducting state breaking. The wires show
the change of the area penetrated by the magnetic field lines
in the HTS. The HTS with pinned magnetic field lines of the
NdFeB sintered ring magnet is, (a) put below the wires, andabove the 100mm cubic NdFeB sintered magnet in the room
temperature, (b) warming in the room temperature, and (c)at the temperature of normal state.

netic field and temperature dependence of pinning effectthrough this observation with mesurering the temperature of the HTS, varing the external magnetic field, andso on.
III.

CONCLUSION

It was shown the very simple method to observe themagnetic field lines for the Meissner effect as well as forthe pinning effect. The author prepared some movies on a
webpage[13]. The movies have much more plentiful sup-ply of information than the photographs in this article.
Even the beginners can clearly observe the behavior of
the magnetic field lines related superconductivity. Thisobservation is effective for the beginners. In fact, many
visitors in Osaka Science Museum enjoy not only the unexpected phenomena of the interaction between a superconductor and a magnet such as Fig. 1 and Fig. 2, butalso considering the interaction based on the magnetic
field lines. Thus the beginners enjoy the essence of superconductivity. This observation must be useful at any
introduction of superconductivity because the method isvery simple and easy to set up and to use, and the phenomena is enough large and clear to demonstrate with

the naked eye.

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Acknowledgments

The author would like to express his gratitude to Nippon Steel Corporation and Dr. Hidekazu Teshima (Advanced Technology Research Laboratories, Nippon SteelCorporation). Nippon Steel Corporation sympathizedwith the author’s design of the demonstration and supplied the GdBaCuO bulk HTS. Dr. H. Teshima copedwith the difficulties for the author.