Proposal of a mathematical model to evaluate
the effects of magnetic radiation applied as
growth stimulation of beet (Beta vulgaris) seeds
Propuesta de un modelo matemático para evaluar los
efectos de la radiación magnética aplicada como
estimulación de crecimiento de semillas de remolacha (Beta
vulgaris)
Jefferson Manuel Valencia Jimenez
1
Fabian Roberto Allauca Pancho
2
Andrés Fernando Morocho Caiza
3
Lenin Patricio Jiménez Pozo
4
Abstract: The human population has a constant growth which
creates a great demand for volumes of quality food free of chemical
fertilizers, then it is of vital importance to optimize the production
processes. Magnetism was chosen as a source of radiation to stimulate
the growth of beet seeds. This vegetable was chosen because in
studies carried out it was detected that beets are an important source
of vitamins and minerals, especially for sports of high physical effort
such as cycling. To carry out this study we have coils capable of
generating 10mT, 20mT and 30mT. The seeds were exposed for 1min,
10min, 30min, following an experimental design. The seeds were
sown and monitored recording the data of both irradiated and control
seeds. The data obtained were organized for the respective statistical
analysis and to obtain a proposal of a mathematical model that
represents the experiment. A benefit in plant growth of up to 2.5 cm
was obtained using 30 mT radiation with respect to the control group
seeds.
Keywords: Seed germination, electricity, electronics,
electromagnetism, coils, sugar beets.
1
Engineer in Electronics Control and Industrial
Networks. National University of Chimborazo
(UNACH), jefferson.valencia@educacion.gob.ec
https://orcid.org/0009-0004-2388-7019
2
Mechanical Engineer, Master's Degree in
Operations Management, Master's Degree in
Mathematics with mention in Modeling and
Teaching
Escuela Superior Politécnica de Chimborazo
(ESPOCH), fabian.allauca@espoch.edu.ec
https://orcid.org/0000-0001-7668-3053
3
Engineer in Electronics Control and Industrial
Networks, Master in Mathematics, mention in
Modeling and Teaching. Polytechnic School of
Chimborazo (ESPOCH)
andres.morocho@espoch.edu.ec
https://orcid.org/0000-0003-3146-8784
4
Forestry Engineer, Master in Sustainable Forest
Management.
University of the Armed Forces ESPE
ljimenez@espe.edu.ec
https://orcid.org/0009-0002-4523-8541
Published
Instituto Tecnológico Superior Edwards
Deming. Quito – Ecuador
Periodicity
January-March
Vol. 1, Num. 20, 2024
pp. 44- 57
http://centrosuragraria.com/index.php/revista
Dates of receipt
Received: October 09, 2023
Approved: December 19, 2023
Correspondence author
jefferson.valencia@educacion.gob.ec
Creative Commons License
Creative Commons License, Attribution-
NonCommercial-ShareAlike 4.0
International.https://creativecommons.org/lice
nses/by-nc-sa/4.0/deed.es
January - March vol. 1. Num. 1 - 2024
45
Resumen: La población humana tiene un crecimiento constante por
lo que se crea una gran demanda de volúmenes de alimentos de
calidad libres de fertilizantes químicos, entonces es de vital
importancia la optimización de los procesos de producción. Se
escogió al magnetismo como fuente de radiación para estimular el
crecimiento de semillas de remolacha siendo este vegetal escogido
porque en estudios realizados se detectó que la remolacha es una
fuente importante de vitaminas, minerales en especial para deportes
de alto esfuerzo físico como el ciclismo. Para realizar dicho estudio
se cuenta con bobinas capaces de generar 10mT, 20mT y 30mT. Se
expusieron a las semillas durante 1min, 10min, 30min, siguiendo un
diseño experimental. Las semillas se sembraron y monitorearon
registrando los datos tanto de las irradiadas, así como las semillas
testigo. Se organizaron los datos obtenidos para el respectivo análisis
estadístico y obtención de una propuesta de modelo matemático que
representa el experimento. Se obtuvo un beneficio en el crecimiento
de las plantas de hasta 2.5 cm usando la radiación de 30 mT con
respecto a las semillas del grupo de control.
Palabras clave: Germinación de semillas, electricidad,
electrónica, electromagnetismo, bobinas, remolacha.
Introduction
The wear and deterioration of arable soil in the world is alarming due
to the indiscriminate use of chemical fertilizers; therefore, research is
being carried out with alternative methods for the improvement of crops
in a less invasive way, one of them being physical methods such as
magnetic radiation (Ruiz et al., 2015).
Thus, food security and agricultural sustainability emerge as crucial
challenges in contemporary society. The growing demand for high
quality food, free of pesticides and chemical fertilizers, poses an
unwavering urgency in the search for innovative solutions to improve
agricultural production in an efficient and environmentally friendly
manner (Burbano-Orjuela, 2016).
Agriculture, as one of the fundamental pillars of human survival, is at a
crossroads (De Medeiros et al., 2015) .The balance between the demand
for food and the need to preserve natural resources and biodiversity has
become increasingly delicate (Diaz et al., 2015) .In this context,
agricultural research plays an essential role by exploring novel and
sustainable approaches for growing high quality food.
One of the recent approaches that has attracted considerable attention is
the application of magnetic radiation to stimulate crop growth
(Domínguez-Pacheco et al., 2010). This approach is based on the use of
controlled magnetic fields to influence specific biological processes in
Optimization and redesign of the Santo Domingo leachate treatment plant: an approach to
environmental efficiency and sustainable development
46
plants. As the understanding of the interactions between magnetism and
biology deepens, it opens a promising avenue for improving
agricultural production and, at the same time, reducing dependence on
chemical inputs.
In this context, beet (Beta vulgaris) stands out as a crop of particular
interest. Beyond its nutritional value, beet has been highlighted as an
important source of vitamins and minerals, making it a valuable food
resource. In addition, its relevance extends to high-performance sports,
such as cycling, where its ability to provide significant benefits in terms
of endurance and health has been recognized.
Agriculture in Ecuador is one of the most important sectors of the
country's economy, so it should follow the trend of developed countries
in the field of radiation research as a source for the improvement and
quality of products (León et al., 2020). (León et al., 2020).
The purpose of this study is to indicate that magnetic radiation is a
beneficial alternative physical method that is environmentally friendly
for the stimulation of beet seed growth; by means of an experimental
study, in which the data will be analyzed statistically to propose a
mathematical model that describes the experiment.
Regarding similar studies is the one by Hołubowicz et al. (2014) who
conclude that low frequency magnetic field (LFMF) of 20 mT, used for
12 h to soak onion seeds of 'Octavia' and 'Eureka' varieties in distilled
water at 20 °C, resulted in an increase in their germination rate. The
germination energy for both varieties increased from 75.8 % and 65 %
(control) to 88.3 % and 87.5 %, respectively. As for germination
capacity, for the 60 min treatment with LFMF in the same varieties, it
increased from 85 % and 76.3 % (control) to 92 % and 90 %,
respectively. These phenomena were accompanied by an increase in
seedling length from 5.3 cm and 4.2 cm (control) to 8.4 cm and 5.7 cm,
respectively. The use of LFMF increased the field emergences of seeds
of the onion variety 'Octavia'. Especially for seeds treated for 60 min,
significant differences were observed compared to control plants.
However, no differences were found in terms of their emergence in the
field for the 10 and 30 minute treatments. The use of LFMF for 60
minutes on 'Octavia' onion seeds increased their emergences in the field
and root length in the bulbs. The LFMF used had no effect on the dry
matter of bulbs grown from seeds when exposed to 10- and 30-minute
January - March vol. 1. Num. 1 - 2024
47
treatments, but when exposed to a 60-minute treatment, dry matter
decreased and the amount of quercetin content increased.
In his research, Moussa (2011) observes that exposure of onion seeds
to a magnetic field of 20 mT for 12 hours, combined with a temperature
of 20 °C, leads to a significant increase in germination rate and seedling
growth. Likewise, the use of magnetized water at 30 mT demonstrates
the ability to improve both the quantity and quality of common bean
crops, suggesting a stimulation in the defense system, photosynthetic
activity and efficiency in the translocation of photoassimilates in these
plants.
These findings point to a promising research path, but also underline
the need to understand in detail the mechanism behind the effects of
magnetic fields on agriculture. It is therefore crucial to explore this area
with interdisciplinary collaborations between physicists, biologists and
physiologists. Although initial results are encouraging, it is essential to
conduct more extensive and detailed research on a variety of crops to
fully assess the potential of this technique in improving agriculture.
Other research has demonstrated the sensitivity of plants to variations
in the geomagnetic field (GMF) (Occhipinti et al., 2014), which arouses
deep scientific interest. Despite progress in understanding the
mechanisms underlying the GMF effect in animals, in particular with
the proposal of cryptochrome as a possible magnetoreceptor, the
influence of GMF on plant evolution remains an enigma. Records of
changes in GMF magnetic polarity throughout Earth's history, which
coincide with times of angiosperm diversification, suggest an intriguing
connection.
With this background, beet was selected for the research since its
benefits are comparable to industrialized energy drinks in the sports
field (Aragon, 2020).
In Ecuador, agriculture represents the second source of income of the
country and contributes significantly to the Gross Domestic Product
(GDP). Therefore, research in this field is of great importance to
improve crop yields in a sustainable and environmentally friendly
manner (León, et al., 2020).
Likewise, magnetic radiation has attracted increasing interest, as the
effect of stationary magnetic fields generated by permanent magnets or
DC-powered coils is evaluated in agricultural applications, including
Optimization and redesign of the Santo Domingo leachate treatment plant: an approach to
environmental efficiency and sustainable development
48
the stimulation of plant germination and growth (Garcés et al., 2017).
as well as the increase in biomass volume. The radiation values
considered in the studies vary from 5 milli Teslas to 500 milli Teslas,
equivalent to 50 Gauss to 5000 Gauss, with different exposure times
depending on the sensitivity of plants to magnetic fields (Ruiz et al.,
2015) .
In parallel, there has been growing interest in beet juice (BRJ) due to its
NO3 nitrate content, which has been associated with physiological
benefits that may improve physical performance, including increased
resistance to muscle fatigue (Rojas Valverde, et al., 2020).
In the following section, the theoretical concepts necessary to
understand and design an electromagnet that works as a magnetic
radiation chamber will be presented.
A magnetic field along a closed path is equal to the sum of currents
passing through a surface.
If there are N turns each carrying current i, the sum of currents will be
equal to the product of N*i. This product is known as the
magnetomotive force (m.m.f.) (Fraile Mora, 2008, p. 8).
! "
#
$
Magnetic permeability
%&'(# " )*(+,-($ " .*(# " /$
Ampere's Law in differential form
0$123
!
" 4.125 " 6
"
" 718
Ampere's Law in integral form
Where:
B = Magnetic induction is measured in Teslas. [T]
H = Magnetic field [A9v/m]
J = Current density [A/m].
N = Number of turns
January - March vol. 1. Num. 1 - 2024
49
i = electric current
Magnetic flux represents the number of magnetic field lines passing
through a surface and is defined by the following formula: (Fraile Mora,
2008, p. 9).
: " 0# 125
#
Where:
: = Magnetic flux is measured in Weber [wb] = Magnetic flux is
measured in Weber [wb].
The inductance in a coil or electromagnet is the ratio between the
magnetic flux and the electric current intensity, its formula is as
follows: (Fraile-Mora, 2008, p. 31)
; "
:
&
L = inductance is measured in Henries [H].
Magnetic flux density is the relationship between a magnetic flux and a
surface area, its formula is: (Fraile-Mora, 2008, p. 48)
# "
:
<
Where:
S = Surface area [m2].
Harold Wheeler's formula for calculating the inductance of a coil:
; " )=>?@(
A
$
7
$
B?ACD)EF
Where:
a = Radius
b = Coil length
Optimization and redesign of the Santo Domingo leachate treatment plant: an approach to
environmental efficiency and sustainable development
50
N = Number of turns
The geomagnetic field is static, homogeneous (for most and relatively
weak (35 µT near the equator, 70 µT near the Earth's magnetic poles).
The common unit for "magnetic flux density" (B) is 1 T (Tesla), defined
as: (Galland, and Pazur, 2005, p. 371-373).
DG " D
H95
I
$
" D
JK
5
$
9L
Electromagnetic energy acts on matter and interrelates with biological
organisms at each stage of development from germination, and
therefore can be a low-cost technique to improve seed quality
(Domínguez Pacheco, 2010, p. 183).
With the objective of evaluating the effect of the application of
electromagnetic radiation on germination and seed growth. They will
be exposed to electromagnetic fields with an intensity of 1uT to 0.098T
for 10, 20 and 30 minutes to make a comparison with control seeds
(Armando et al, 2019).
The results will be organized in a database to be processed with
statistical methods or Big Data techniques to obtain the respective
conclusions.
In order to establish a mathematical model describing the relationship
between growth time and plant height, a third degree polynomial
regression was performed, which is the best fit to the data obtained in
the experiment. The polynomial model was expressed as follows:
$
B
-
F
" A-
%
CE-
$
CM-C%
Where:
$
B
-
F
represents plant height as a function of time in days.
B
-
F
.
ANENMN%(are regression coefficients that were determined by statistical
analysis.
After performing the third-degree polynomial regression fit to the data
provided, the following model coefficients were obtained:
January - March vol. 1. Num. 1 - 2024
51
A " )=))O>
E " )=)P)D
M " )=?P>Q
% " D=O)PR
The resulting mathematical model describing the relationship between
growth time and height of beet plants irradiated at 30mT is:
$
B
-
F
" )=))O>-
%
C)=)P)D-
$
C)=?P>Q-CD=O)PR
Under this perspective, in the field of agricultural research, the
application of magnetic radiation as a growth stimulation technique in
sugar beet seeds has aroused growing interest. The main objective of
this paper is to propose a comprehensive mathematical model that
allows us to accurately evaluate the effects of magnetic radiation on the
growth of these seeds. This general objective will guide our research
and will allow us to explore in depth the effects of magnetic radiation
on the growth of beet seeds. The control plants with respect to the plants
subjected to magnetic irradiation?
Materials and methods
An experimental study was conducted to investigate the effects of
different magnetic field levels on seed and plant germination, growth
and mortality. Three levels of magnetic field exposure were used: 30
mT, 20 mT and 10 mT, along with three exposure durations: 30 min, 10
min and 1 min. Two control groups were established for comparison.
Seeds of the same species were selected and divided into groups
according to the levels and duration of exposure to the magnetic field.
The seeds were kept in laboratory conditions with controlled
temperature and humidity until the beginning of the experiment.
The seeds were subjected to magnetic fields using a device specifically
designed for this purpose. Magnetic fields of 30 mT, 20 mT and 10 mT
were applied for 30 min, 10 min and 1 min, respectively. The exposures
were performed in separate groups to ensure the accuracy of the results.
Two control groups were not exposed to any magnetic field.
Optimization and redesign of the Santo Domingo leachate treatment plant: an approach to
environmental efficiency and sustainable development
52
After exposure to the magnetic field, seeds were sown under laboratory
conditions in culture trays. The time required for germination of each
seed in each experimental and control group was recorded. Germination
rate was calculated as the percentage of seeds that germinated
successfully.
Seedlings from the seeds were planted in individual pots and
maintained in a greenhouse under controlled conditions of light,
temperature and humidity for 16 days. The height of each plant was
measured in centimeters and average values were recorded for each
experimental and control group.
During the 16-day growing period, plant mortality was recorded for
each experimental and control group. Plants showing signs of wilting,
discoloration or death were counted and the mortality rate was
calculated as the percentage of plants that died.
Analyses of variance (ANOVA) were performed to compare significant
differences between experimental and control groups in terms of plant
germination, growth and mortality. Post hoc tests were used to identify
specific differences between groups. A significance level of p < 0.05
was considered.
This study was conducted in compliance with all applicable ethical and
animal welfare regulations. It was ensured that the magnetic field
exposure conditions did not cause unnecessary harm or suffering to the
plants. Established protocols for handling and care of the plants in the
greenhouse were followed.
3. Result
Seed sprouting
Table 1: Seeds exposed to different levels of magnetic fields
Outbreak
30mT
-
30mi
n
1
1
1
1
1
1
1
1
1
1
10
40
100
1
1
1
1
1
1
1
1
1
1
10
January - March vol. 1. Num. 1 - 2024
53
1
1
1
1
1
1
1
1
1
1
10
1
1
1
1
1
1
1
1
1
1
10
30mT-
10min
1
1
1
0
1
1
1
1
1
1
9
36
90
1
1
1
0
1
1
0
1
1
1
8
1
1
1
1
1
1
1
1
1
1
10
1
1
1
1
1
1
1
0
1
1
9
30mT-
1min
1
1
1
1
1
1
1
1
1
1
10
39
98
1
1
1
1
0
1
1
1
1
1
9
1
1
1
1
1
1
1
1
1
1
10
1
1
1
1
1
1
1
1
1
1
10
20mT-
30min
1
1
1
1
1
1
1
1
1
0
9
37
93
1
1
1
1
1
1
1
0
1
1
9
1
1
1
1
1
1
1
1
1
0
9
1
1
1
1
1
1
1
1
1
1
10
20mT-
10min
0
0
1
1
1
1
1
1
1
1
8
37
93
1
1
1
1
1
1
1
1
1
1
10
1
1
1
1
1
1
1
1
1
1
10
1
1
1
1
0
1
1
1
1
1
9
20mT
-1min
1
1
1
1
1
1
1
1
1
1
10
19
48
1
1
1
1
1
1
1
1
1
0
9
Table 2: Control seeds
Outbreak
Control
1
1
1
1
1
1
1
0
1
0
8
34
85
1
1
1
1
0
1
0
1
1
1
8
0
1
1
1
1
1
1
1
1
1
9
1
1
1
1
1
1
1
1
1
0
9
30mT-
10min
1
1
1
1
1
1
1
1
1
1
10
32
80
1
1
1
0
0
1
1
1
0
1
7
1
1
1
1
1
1
1
0
0
0
7
0
1
1
0
1
1
1
1
1
1
8
00mT-
10min
1
1
1
1
1
0
1
1
1
0
8
34
85
1
1
0
1
1
1
1
1
1
0
8
1
1
1
1
1
1
0
1
1
1
9
1
1
1
1
1
1
1
1
1
0
9
10mT-
1min
1
0
1
1
1
0
1
1
1
1
8
32
80
0
1
1
1
1
1
1
1
1
1
9
1
0
1
1
1
1
1
1
0
0
7
Optimization and redesign of the Santo Domingo leachate treatment plant: an approach to
environmental efficiency and sustainable development
54
0
1
1
1
1
1
0
1
1
1
8
Control
1
0
1
1
1
0
1
1
1
1
8
37
93
1
1
1
1
1
1
1
1
1
1
10
1
1
1
1
1
1
1
1
1
1
10
0
1
1
1
1
1
1
1
1
1
9
20mT
-1min
1
1
1
1
0
1
1
1
1
0
8
17
43
1
1
1
1
1
1
1
1
1
0
9
It was observed that seeds exposed to different levels of magnetic field
(30 mT, 20 mT and 10 mT) reacted variably in terms of sprouting. Seeds
exposed to 30 mT for 30 minutes showed the highest sprouting rate,
reaching 100%. Those exposed to 10 min at 30 mT sprouted at 90%,
while those exposed to 1 min at the same intensity reached 88%
sprouting. Similarly, for the group exposed to 20 mT, seeds exposed for
30 min sprouted 93%, while those exposed to 10 min and 1 min
sprouted 90% and 88%, respectively. As for the 10 mT group, sprouting
rates were 80% for all three exposures. In comparison, control seeds in
the two groups achieved sprouting rates of 85% and 90%, respectively.
Plant growth varied according to the level of exposure to the magnetic
field. In the 30 mT group with 30 min exposure, plants reached an
average height of 8.5 cm, while in the 30 mT group with 10 min
exposure, average growth was 7.5 cm, and in the 1 min group, 7 cm.
For the 20 mT group, the average heights were 7 cm, regardless of
exposure duration. For the 10 mT group, plants exposed for 30 min
reached an average height of 7 cm, while those exposed for 10 min and
1 min reached a height of 6.5 cm. In the control groups, plants reached
an average height of 6.5 cm in both cases.
A mortality rate was recorded for all magnetic field exposures. In the
30 mT exposed groups, 15% of the plants died. In the 20 mT group, an
increase in mortality of 15% was observed in the 30-min group, 25% in
the 10-min group, and 38% in the 1-min group. In the 10 mT group, a
similar trend was observed, with a mortality rate of 25%, 28% and 43%
for the 30-minute, 10-minute and 1-minute exposures, respectively. In
the control groups, mortality rates of 50% and 45% were recorded for
groups 1 and 2, respectively.
January - March vol. 1. Num. 1 - 2024
55
These results reveal the influence of the magnetic field on plant
germination and growth, as well as its effect on mortality. The observed
differences in plant response to different levels of exposure and
duration suggest the need for further research to fully understand the
effects of magnetic fields on plants.
The results obtained in this study provide valuable information on the
effects of magnetic field exposure on the germination process and plant
growth. In particular, a clear differential response in seed sprouting and
plant development was observed as a function of magnetic field
strength and duration of exposure. These findings have significant
implications for the understanding of plant biology and raise important
questions about the influence of unconventional environmental factors
on plant development.
Seed sprouting results indicate that exposure to magnetic fields can
have a stimulating effect on germination. Interestingly, seeds exposed
to 30 mT for 30 min showed the highest sprouting rate, reaching 100%.
This might suggest that a certain threshold of intensity and duration of
exposure is necessary to maximize germination.
The effect on plant growth is another crucial aspect of this study. It was
found that plants exposed to magnetic fields exhibited differential
growth as a function of intensity and duration of exposure. The most
notable differences were observed in the 30 mT group, where plants
exposed for 30 min reached an average height of 8.5 cm, compared to
plants exposed for 10 min or 1 min, which showed significantly less
growth. This could indicate that prolonged exposure to intense
magnetic fields may have a positive effect on plant growth.
Taken together, these results suggest that exposure to magnetic fields
can have a complex impact on plant germination and growth. These
findings open the door to future research that could help to better
understand the interaction between magnetic fields and biological
systems, as well as their applicability in agriculture and horticulture.
The third degree polynomial model provides an adequate fit to the
observed data. It shows a nonlinear relationship between growth time
and beet plant height, suggesting that growth is not uniform and
undergoes significant changes over time. This may be related to factors
such as nutrient availability, climatic conditions and other
environmental factors that influence plant development.
Optimization and redesign of the Santo Domingo leachate treatment plant: an approach to
environmental efficiency and sustainable development
56
This mathematical model can be useful in predicting beet plant height
as a function of time, which can be valuable for agricultural planning
and crop-related decision making.
4. Conclusions
This study demonstrates that magnetic radiation at a level of 30 mT has
positive effects on plant seeds. Irradiated seeds germinated faster with
a 2-day advantage compared to control seeds, with 100% effectiveness.
In addition, plants resulting from irradiated seeds maintained better
performance during growth, with a 5-day improvement in the tuber
harvesting process. These plants also exhibited stronger growth, both in
height and in thickness and color. These results suggest that magnetic
radiation may play an important role in improving plant development
and agriculture in general. In this study, a third-degree mathematical
model describing the relationship between growth time in days and
height of beet plants has been established. This model provides a useful
tool for understanding and predicting the growth of beet plants over
time. However, further research is recommended to explore the
underlying causes of variability in plant growth and to validate the
model under different environmental conditions and beet varieties.
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