Using a single loop solenoid motion of a magnetic granular particle is observed through its induced emf voltage, which is simulated using Faraday-Lenz induction law and model of magnetic dipole. Position of the loop is important, especially for this special case free fall and stationary base, where the maximum height is reduced in time. Some special moment, such as the particle reaching maximum height and hitting the base can be identified from the induce emf voltage curve. Other version https://osf.io/ks2za/

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Induced Current Simulation of One-
Dimensional Vibrating Magnetic Granular
Particles System: Free Fall of Single Magnetic
Granular Particle Hitting Stationary Base
Sparisoma Viridi1
, Suprijadi2
Departemen of Physics, Faculty of Mathematics and Natural Sciences
Research Center for Nanosciences and Nanotechnology
Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia
1
dudung@fi.itb.ac.id, 2
supri@fi.itb.ac.id

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Outline
• Introduction
• Measurement system, theory, simulation
• Results and discussion
• Summaries

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Introduction:
Granular materials

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Granular materials
• We interact daily with this kind of materials,
e.g sugar, salt, coffee, sand, gravel, etc.
• It is considered to be a solid, liquid, or gas –
depends on supplied energy in the form of
vibration.
• It is a dissipative system, without supplied
energy it tends to be (critically) solid.

5. Solid and liquid (3d system)
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H. M. Jaeger, S. R. Nagel, R. P. Behringer, "Granular solid, liquids, and gases", Reviews of Modern Physics 68 1259
(1996).
solid
liquid

6. Liquid and gas (2d system)
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P. Ehuis, K. van der Weele, D. van der Meer, D. Lohse, "Granular leidenfrost effect: Experiment and theory of floating
particle clusters", Physical Review Letters 95 258001 2005.

7. Resonance (1d system)
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C. R. K. Windows-Yule1, A. D. Rosato, A. R. Thornton, D. J. Parker, "Resonance effects on the dynamics of dense
granular beds: Achieving optimal energy transfer in vibrated granular systems", New Journal of Physics 17 023015
2015.
S = ω2
A2
/gd = 1.83,
N = 20,
observed using γ-ray
f = 13.4 Hz
f = 25.1 Hz

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Introduction:
Simulation of experiment

9. Determination of detector angle
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S. Viridi, Hendro, "Model and Visualization of Ray Tracing using JavaScript and HTML5 for TIR Measurement System
Equipped with Equilateral Right Angle Prism", Prosiding of the 2nd Indonesian Student Conference on Science and
Mathematics (ISCSM-2), Eds. M. A. Martoprawiro et al., Bandung, Indonesia, 11-12 October 2013, pp. (in review) |
arXiv:1310.3335v1 [physics.optics] Sat,12 Oct 2013.

10. Determination of detector .. (cont.)
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Hendro, S. Viridi, Y. Pratama, "Determination of Detector Rotation Angle in the Experiment based on the Total Internal
Reflection using an Equilateral Right Angle Prism", in The 5th Asian Physics Symposium-2012, edited by S. Viridi et
al., AIP Conference Proceedings 1656, American Institute of Physics, Melville, NY, 2015, pp. 040012.
( )
( )




>−
=
<+
=
.,2
,,2
,,2
4
1
4
1
4
1
πψψψ
πψψ
πψψψ
φ
d
d
( ) ?=ψd

11. EMF of moving magnet
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S. Viridi, S. N. Khotimah, Khairurrijal, "Profile in a Circular Loop Passing a Limited Rectangular Area with Perpendicular
Uniform Constant Magnetic Field", arXiv:1201.3489v1 [physics.class-ph] Tue, 17 Jan 2012.
H. R. Fandia, Y. Rusmiati, S. N. Khotimah, "Penentuan Kecepatan Sudut Benda Berotasi dengan Menggunakan
Prinsip Listrik Magnet", Prosiding Seminar Kontribusi Fisika 2011 (SKF 2011), Eds. F. D. E. Latief et al., Bandung,
Indonesia, 1-2 Desember 2011, pp. 107-112.

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Measurement system,
theory, simulation

13. Measurement system
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One-dimensional particle
stacking with at least one
magnetic grain (PS),
vibrator (VB), signal
generator (SG), signal
amplifier (SA), induction
coil (IC), and a digital
voltmeter or oscilloscope
(OS) construct the
measurement system

14. Theory
• Magnetic field from a dipole in a grain
• Induced current and magnetic flux
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( ) ( )θθθ
π
µ ˆsinˆcos2
4 3
0
+= r
r
M
rB

dt
d BΦ
−=indε ∫ ⋅=Φ AdBB


15. Theory (cont.)
• Induction at coil i due to
grain j
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















+
⋅−=
j
ij
ij
jj
ij
ji
ij
z
v
z
MA
θθω
π
µ
ε
cos3sin
2 3
0

16. Simulation
• Free fall and multiple
bounce
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Results and discussion

18. Values are in several orders + / -
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19. Proposed formula
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( )
( )




>
<−
=
.0,log
,0,0
.0,log
indind
indind
log
εε
εε
ε

20. Change of dipole direction
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21. Dipole change Δθ = π/8
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22. Dipole change Δθ = π/4
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23. Dipole change Δθ = π/2
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24. State A  B
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Summaries

26. Summaries
• Results from this simulation can be used to
plan a fully integrated and appropriate
experimental setup, especially in order of
induced emf ε which also alters its sign.
• Measureable value of ε can be advanced by
choosing the right value of A and M according
to unit of μ0MA/2π.
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27. Summaries (cont.)
• Induced emf voltage for a single magnetic
granular particle exibits a free fall and an
elastic bounching to vibrator stationary base
through a coil has been simulated.
• The moment where the particle hitting
stationary base and it reaching maximum
height can be identified from the emf voltage
curve, while the moment it passing loop
position is still unclear.
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28. Acknowledgements
• This work is supported by Kemenristekdikti
research program in 2018
• Presentation of this work is supported by
DAAD and Committee of AEMT 2018
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https://osf.io/ks2za/

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Thank you