Dirac-Maxwell’s equations, retained for magnetic monopoles, are generalized by introducing
magnetic scale field. It allows the magnetic monopoles to be time-dependent and the potentials to be Lorentz
gauge free. The non-conserved part or the time-dependent part of the magnetic charge density is responsible to
produce the magnetic scalar field which further contributes to the magnetic and electric vector fields. This
contribution makes possible to create an ideal square wave magnetic field from an exponentially rising and
decaying magnetic charge.
Optical Aberration is the phenomenon of Image Distortion due to Optics Imperfection.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations visit my website at http://www.solohermelin.com.
This presentation is in the Optics Folder. Since some of the Figures were not downloaded I recommend to see the presentation on my website.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Aerodynamics Part II of 3 describes aerodynamics of bodies in supersonic flight.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
Physics of optics, part ii.
Please send comments and suggestions for improvements to solo.hermelin@gmail.com. Thanks.
For more presentations in optics and other subjects please visit my website on http://solohermelin.com.
Optical Aberration is the phenomenon of Image Distortion due to Optics Imperfection.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations visit my website at http://www.solohermelin.com.
This presentation is in the Optics Folder. Since some of the Figures were not downloaded I recommend to see the presentation on my website.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Aerodynamics Part II of 3 describes aerodynamics of bodies in supersonic flight.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
Physics of optics, part ii.
Please send comments and suggestions for improvements to solo.hermelin@gmail.com. Thanks.
For more presentations in optics and other subjects please visit my website on http://solohermelin.com.
Maxwell equations and propagation in anisotropic mediaSolo Hermelin
Describes the propagation of electromagnetic waves in anisotropic electrical media.
Please send comments to solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
The presentation is not properly downloaded. Please go to my website and open it in the Optics Folder.
Describes the general solutions of Electromagnetic Maxwell Equations.
Intended or Graduate Students in Science (math, physics, engineering) with previous knowledge in electromagnetics.
Please send me comments and suggestions for improvements to solo.hermelin@gmail.com.
More presentations can be found in my website at http://www.solohermelin.com.
Charge Quantization and Magnetic MonopolesArpan Saha
This talk, given as a part of the Annual Seminar Weekend 2011, IIT Bombay, dealt with a homotopy-based
variant of the argument Dirac provided to show that the existence of a single magnetic monopole in the Universe
is a sufficient condition for the quantization of electric charge.
Chiral Transverse Electromagnetic Waves with E H i to study Circular Dichroisminventionjournals
It is shown that a general class of transverse electromagnetic waves with E H i can be obtained. These waves possess magnetic helicity and chirality. This condition is important to excitation of nano molecules when it is necessary consider a global factor as the product of the parameter of optical chirality with the inherent enantiometric properties of the material. The absorption of a chiral molecule in a chiral electromagnetic field is proportional to the imaginary part of mixed electric-magnetic dipole polarizability of the molecules, which determines the circular dichroism, CD of molecules. Chiral fields with different handedness can be used to obtain basic information from the interaction fields-molecules with high optical chirality, having chiral hot spots in nodes of stationary waves with parallel components of electric and magnetic fields.
Description of Physics of Optics, part I.
Please send comments and suggestions for improvements to solo.hermelin@gmail.com. Thanks.
For more presentations in optics and other subjects please visit my website at http://www,solohermelin.com.
I am Ben R. I am a Statistics Assignment Expert at statisticshomeworkhelper.com. I hold a Ph.D. in Statistics, from University of Denver, USA. I have been helping students with their homework for the past 5 years. I solve assignments related to Statistics.
Visit statisticshomeworkhelper.com or email info@statisticshomeworkhelper.com.
You can also call on +1 678 648 4277 for any assistance with Statistics Assignment.
[Electricity and Magnetism] ElectrodynamicsManmohan Dash
We discussed extensively the electromagnetism course for an engineering 1st year class. This is also useful for ‘hons’ and ‘pass’ Physics students.
This was a course I delivered to engineering first years, around 9th November 2009. I added all the diagrams and many explanations only now; 21-23 Aug 2015.
Next; Lectures on ‘electromagnetic waves’ and ‘Oscillations and Waves’. You can write me at g6pontiac@gmail.com or visit my website at http://mdashf.org
I am Irene M. I am an Electromagnetism Assignment Expert at eduassignmenthelp.com. I hold a Ph.D. in Electromagnetism, from California, USA. I have been helping students with their homework for the past 8 years. I solve assignments related to Electromagnetism.
Visit eduassignmenthelp.com or email info@eduassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Electromagnetism Assignments.
Network Lifetime Analysis of Routing Protocols of Short Network in QualnetIOSR Journals
Abstract: A Mobile Ad-Hoc Network (MANET) is a collection of wireless mobile nodes that communicates with each other without using any existing infrastructure, access point or centralized administration. Mobile ad-hoc network have the attributes such as wireless connection, continuously changing topology, distributed operation and ease of deployment. In this paper we have compared the energy consumption of reactive, proactive & hybrid routing protocol AODV,DSR,RIP & ZRP by using different mobility model. We have analyzed the Network lifetime of protocols by varying pay load, mobility, pause time and type of traffic (CBR). A detailed simulation has been carried out in qualnet. The metrics used for performance analysis are energy consumed & battery consumption. It has been observed that RIP has better network lifetime than other.
Maxwell equations and propagation in anisotropic mediaSolo Hermelin
Describes the propagation of electromagnetic waves in anisotropic electrical media.
Please send comments to solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
The presentation is not properly downloaded. Please go to my website and open it in the Optics Folder.
Describes the general solutions of Electromagnetic Maxwell Equations.
Intended or Graduate Students in Science (math, physics, engineering) with previous knowledge in electromagnetics.
Please send me comments and suggestions for improvements to solo.hermelin@gmail.com.
More presentations can be found in my website at http://www.solohermelin.com.
Charge Quantization and Magnetic MonopolesArpan Saha
This talk, given as a part of the Annual Seminar Weekend 2011, IIT Bombay, dealt with a homotopy-based
variant of the argument Dirac provided to show that the existence of a single magnetic monopole in the Universe
is a sufficient condition for the quantization of electric charge.
Chiral Transverse Electromagnetic Waves with E H i to study Circular Dichroisminventionjournals
It is shown that a general class of transverse electromagnetic waves with E H i can be obtained. These waves possess magnetic helicity and chirality. This condition is important to excitation of nano molecules when it is necessary consider a global factor as the product of the parameter of optical chirality with the inherent enantiometric properties of the material. The absorption of a chiral molecule in a chiral electromagnetic field is proportional to the imaginary part of mixed electric-magnetic dipole polarizability of the molecules, which determines the circular dichroism, CD of molecules. Chiral fields with different handedness can be used to obtain basic information from the interaction fields-molecules with high optical chirality, having chiral hot spots in nodes of stationary waves with parallel components of electric and magnetic fields.
Description of Physics of Optics, part I.
Please send comments and suggestions for improvements to solo.hermelin@gmail.com. Thanks.
For more presentations in optics and other subjects please visit my website at http://www,solohermelin.com.
I am Ben R. I am a Statistics Assignment Expert at statisticshomeworkhelper.com. I hold a Ph.D. in Statistics, from University of Denver, USA. I have been helping students with their homework for the past 5 years. I solve assignments related to Statistics.
Visit statisticshomeworkhelper.com or email info@statisticshomeworkhelper.com.
You can also call on +1 678 648 4277 for any assistance with Statistics Assignment.
[Electricity and Magnetism] ElectrodynamicsManmohan Dash
We discussed extensively the electromagnetism course for an engineering 1st year class. This is also useful for ‘hons’ and ‘pass’ Physics students.
This was a course I delivered to engineering first years, around 9th November 2009. I added all the diagrams and many explanations only now; 21-23 Aug 2015.
Next; Lectures on ‘electromagnetic waves’ and ‘Oscillations and Waves’. You can write me at g6pontiac@gmail.com or visit my website at http://mdashf.org
I am Irene M. I am an Electromagnetism Assignment Expert at eduassignmenthelp.com. I hold a Ph.D. in Electromagnetism, from California, USA. I have been helping students with their homework for the past 8 years. I solve assignments related to Electromagnetism.
Visit eduassignmenthelp.com or email info@eduassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Electromagnetism Assignments.
Network Lifetime Analysis of Routing Protocols of Short Network in QualnetIOSR Journals
Abstract: A Mobile Ad-Hoc Network (MANET) is a collection of wireless mobile nodes that communicates with each other without using any existing infrastructure, access point or centralized administration. Mobile ad-hoc network have the attributes such as wireless connection, continuously changing topology, distributed operation and ease of deployment. In this paper we have compared the energy consumption of reactive, proactive & hybrid routing protocol AODV,DSR,RIP & ZRP by using different mobility model. We have analyzed the Network lifetime of protocols by varying pay load, mobility, pause time and type of traffic (CBR). A detailed simulation has been carried out in qualnet. The metrics used for performance analysis are energy consumed & battery consumption. It has been observed that RIP has better network lifetime than other.
“Recurrent Lower Abdomen Pain, An Introspection.”IOSR Journals
Abstract: Introduction: Recurrent Pain Lower Abdomen, („RLAP‟), With/Without Previous Appendecectomy & Or Other Surgeries, Comprise Large No. Of Patients Being Treated Indiscriminately For Years, Without Proper Diagnosis. Aims/Objctive: The Several Variable Aetio-Pathogenesis Factors & Management Modalities, In Different Age, Sex,Occupational,Socio-Economic,Geographical Group Patients, „RLAP‟Studied Under Broad Categorization Of,Post- Appendecectomy Cases(Or Other Surgery);Group „A‟ & Without Prior Appendecectomy(Surgery); Group „B‟. Methods: The Comparative Statistical Analysis Of More Than 2500 Cases Of „RLAP-A &B‟, By Meticulous Methodological Discrete Cauasative Factor Diagnosis & Needed Specific Management. Beside Routine Causes Included Obscured But Definitely Causative Clinical Entities:Ileo-Caecal Lesions; Angulations Acute, Obstuse Etc, Caused By Appendicular Stump ? Invagination Leading To Anatomico-Functional Changes, ,Stump Appendicitis, Appedicular Lump Formation Stages, Especially „Catarrhal Appendicitis‟ Maeckel‟s & Other Diverticular Disease Variants, Invaginated Diverticulum Etc, Mobile Caecum,Recurrent Sigmoid Volulus, Adhesions, N. Root Radiculopathy Symptoms & Others. Results: The Discrete Causative Lesion Dx & AppropriateTreatment Plan (Curetive & Or Maximally Palliative), With Secured Sincere Compliance,Formed The Basic Fundamentals For Overall Better Result Outcomes. Conclusion: The Study, Is An Attempt Towards Overall Management Guide-Lines Plan For A Very Common Clinical Dilemma, To Secure Overall Disease Symptom Free Life.
Prevalence of anemia and socio-demographic factors associated with anemia amo...IOSR Journals
Objective: To study the prevalence of anemia and socio-demographic factors associated with anemia among pregnant women attending antenatal hospital. Material and methods: Total 100 pregnant women were selected for the study and the study was carried out from Sep 2011 to Jan 2012. Pretested and prestructured questionnaire was used to collect general information. Blood samples were collected by qualified technician for hemoglobin estimation. Socio-economic classification by B.G. Prasad was adopted. Classification of anemia by WHO was used. Chi-square test was used for statistical analysis. Results: Overall prevalence of anemia among the pregnant women was found to be 63%. Factors such as level of education and socio-economic status were found to be significantly associated with prevalence of anemia. Conclusion: There is a need for realization that health system should focus on various factors that contribute to the occurrence of anemia and include them as important mediators in the National Health Policy.
Prevalence of Hepatitis B Surface Antigen among Undergraduate Students of Gom...IOSR Journals
Incidence of Hepatitis B virus among healthy asymptomatic students in Gombe State University was determined, this was in an effort of providing baseline data on the diseases burden, and the possible risk factors associated with the infection in the study population. A total of 100 serum samples were collected from volunteers and screened using rapid immune chromatographic test kits for Hepatitis B surface antigen (HBsAg). The study revealed that 14% were HBsAg positive. The highest incidence rate of 18.2% (12) was recorded among the age group of 16-25 years, and males recorded the highest incidence rate of 20% (12), indicating that gender but not age might have greater influence on the infection (P= 0.05).
To study the factors effecting sales of leading tractor brands in Haryana (In...IOSR Journals
Every aspect of the economic life in India is influenced by the agriculture. Agriculture contributes nearly 32% of the national income of India and it offers live hood nearly 70% of the total population and the agriculture is influenced by the tractors industry. Tractor industry plays an important role on the development of agriculture. Indian tractor market is very complex so marketer must care in analysing consumer behaviour. Green Revolution in India had its origin in northern India where Haryana is situated. Thus Haryana’s Contribution to Green Revolution in India is the maximum, In 1966-67 production of food grains in Haryana was 2090 thousand tones. In 1970-71 it increased to 3939 thousand tones and in 1994-2000 it further rose to 131 lakh tones, all this due to the development of tractor manufacturing industries like FARMTRAC, HMT, EICHER, TAFE etc. Present work covers studying sales of different tractor brands in Haryana (India) and how various brands have become the choice of agriculturist on the basis of getting experienced by others. The best brand so for is found to be FARMTRAC by agriculturist by the recommendation of relatives who have experinecd the same. It was depicted from the studies that farmers purchasing tractors by recommendations of relatives are not much educated.
Stellar Measurements with the New Intensity FormulaIOSR Journals
In this paper a linear relationship in stellar optical spectra has been found by using a
spectroscopical method used on optical light sources where it is possible to organize atomic and ionic data.
This method is based on a new intensity formula in optical emission spectroscopy (OES). Like the HR-diagram ,
it seems to be possible to organize the luminosity of stars from different spectral classes. From that organization
it is possible to determine the temperature , density and mass of stars by using the new intensity formula. These
temperature, density and mass values agree well with literature values. It is also possible to determine the mean
electron temperature of the optical layers (photospheres) of the stars as it is for atoms in the for laboratory
plasmas. The mean value of the ionization energies of the different elements of the stars has shown to be very
significant for each star. This paper also shows that the hydrogen Balmer absorption lines in the stars follow
the new intensity formula.
Gc-Ms Analysis and Antimicrobial Activity of Essential Oil of Senecio Peduncu...IOSR Journals
The chemical composition of the essential oil obtained from the leaves of Senecio pedunculatus collected from the Kumaon region of Uttarakhand, was analyzed by GC-MS. The major constituent was found out to be caryophyllene oxide (23.28%). The antibacterial and antifungal activity of the oil was determined by disc diffusion method. Results showed that the oil exhibited mild antimicrobial activity.
Classical and Quasi-Classical Consideration of Charged Particles in Coulomb F...ijrap
On the basis of the theory of bound charges the calculation of the motion of the charged particle at the Coulomb field formed with the spherical source of bound charges is carried out. Such motion is possible in
the Riemanniam space-time. The comparison with the general relativity theory (GRT) and special relativity theory (SRT) results in the Schwarzshil'd field when the particle falls on the Schwarzshil'd and Coulomb centres is carried out. It is shown that the proton and electron can to create a stable connection with the dimensions of the order of the classic electron radius. The perihelion shift of the electron orbit in the proton field is calculated. This shift is five times greater than in SRT and when corrsponding substitution of the constants it is 5/6 from GRT. By means of the quantization of adiabatic invariants in accordance with the method closed to the Bohr and Sommerfeld one without the Dirac equation the addition to the energy for the fine level splitting is obtained. It is shown that the Caplan's stable orbits in the hydrogen atom coincide with the Born orbits.
Similar to Electromagnetic fields of time-dependent magnetic monopole (20)
Cancer cell metabolism: special Reference to Lactate PathwayAADYARAJPANDEY1
Normal Cell Metabolism:
Cellular respiration describes the series of steps that cells use to break down sugar and other chemicals to get the energy we need to function.
Energy is stored in the bonds of glucose and when glucose is broken down, much of that energy is released.
Cell utilize energy in the form of ATP.
The first step of respiration is called glycolysis. In a series of steps, glycolysis breaks glucose into two smaller molecules - a chemical called pyruvate. A small amount of ATP is formed during this process.
Most healthy cells continue the breakdown in a second process, called the Kreb's cycle. The Kreb's cycle allows cells to “burn” the pyruvates made in glycolysis to get more ATP.
The last step in the breakdown of glucose is called oxidative phosphorylation (Ox-Phos).
It takes place in specialized cell structures called mitochondria. This process produces a large amount of ATP. Importantly, cells need oxygen to complete oxidative phosphorylation.
If a cell completes only glycolysis, only 2 molecules of ATP are made per glucose. However, if the cell completes the entire respiration process (glycolysis - Kreb's - oxidative phosphorylation), about 36 molecules of ATP are created, giving it much more energy to use.
IN CANCER CELL:
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
Unlike healthy cells that "burn" the entire molecule of sugar to capture a large amount of energy as ATP, cancer cells are wasteful.
Cancer cells only partially break down sugar molecules. They overuse the first step of respiration, glycolysis. They frequently do not complete the second step, oxidative phosphorylation.
This results in only 2 molecules of ATP per each glucose molecule instead of the 36 or so ATPs healthy cells gain. As a result, cancer cells need to use a lot more sugar molecules to get enough energy to survive.
introduction to WARBERG PHENOMENA:
WARBURG EFFECT Usually, cancer cells are highly glycolytic (glucose addiction) and take up more glucose than do normal cells from outside.
Otto Heinrich Warburg (; 8 October 1883 – 1 August 1970) In 1931 was awarded the Nobel Prize in Physiology for his "discovery of the nature and mode of action of the respiratory enzyme.
WARNBURG EFFECT : cancer cells under aerobic (well-oxygenated) conditions to metabolize glucose to lactate (aerobic glycolysis) is known as the Warburg effect. Warburg made the observation that tumor slices consume glucose and secrete lactate at a higher rate than normal tissues.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
The increased availability of biomedical data, particularly in the public domain, offers the opportunity to better understand human health and to develop effective therapeutics for a wide range of unmet medical needs. However, data scientists remain stymied by the fact that data remain hard to find and to productively reuse because data and their metadata i) are wholly inaccessible, ii) are in non-standard or incompatible representations, iii) do not conform to community standards, and iv) have unclear or highly restricted terms and conditions that preclude legitimate reuse. These limitations require a rethink on data can be made machine and AI-ready - the key motivation behind the FAIR Guiding Principles. Concurrently, while recent efforts have explored the use of deep learning to fuse disparate data into predictive models for a wide range of biomedical applications, these models often fail even when the correct answer is already known, and fail to explain individual predictions in terms that data scientists can appreciate. These limitations suggest that new methods to produce practical artificial intelligence are still needed.
In this talk, I will discuss our work in (1) building an integrative knowledge infrastructure to prepare FAIR and "AI-ready" data and services along with (2) neurosymbolic AI methods to improve the quality of predictions and to generate plausible explanations. Attention is given to standards, platforms, and methods to wrangle knowledge into simple, but effective semantic and latent representations, and to make these available into standards-compliant and discoverable interfaces that can be used in model building, validation, and explanation. Our work, and those of others in the field, creates a baseline for building trustworthy and easy to deploy AI models in biomedicine.
Bio
Dr. Michel Dumontier is the Distinguished Professor of Data Science at Maastricht University, founder and executive director of the Institute of Data Science, and co-founder of the FAIR (Findable, Accessible, Interoperable and Reusable) data principles. His research explores socio-technological approaches for responsible discovery science, which includes collaborative multi-modal knowledge graphs, privacy-preserving distributed data mining, and AI methods for drug discovery and personalized medicine. His work is supported through the Dutch National Research Agenda, the Netherlands Organisation for Scientific Research, Horizon Europe, the European Open Science Cloud, the US National Institutes of Health, and a Marie-Curie Innovative Training Network. He is the editor-in-chief for the journal Data Science and is internationally recognized for his contributions in bioinformatics, biomedical informatics, and semantic technologies including ontologies and linked data.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
A brief information about the SCOP protein database used in bioinformatics.
The Structural Classification of Proteins (SCOP) database is a comprehensive and authoritative resource for the structural and evolutionary relationships of proteins. It provides a detailed and curated classification of protein structures, grouping them into families, superfamilies, and folds based on their structural and sequence similarities.
Professional air quality monitoring systems provide immediate, on-site data for analysis, compliance, and decision-making.
Monitor common gases, weather parameters, particulates.
Electromagnetic fields of time-dependent magnetic monopole
1. IOSR Journal of Applied Physics (IOSR-JAP)
e-ISSN: 2278-4861.Volume 5, Issue 1 (Nov. - Dec. 2013), PP 55-58
www.iosrjournals.org
www.iosrjournals.org 55 | Page
Electromagnetic fields of time-dependent magnetic monopole
G. H. Jadhav
(Department of Physics, Shri Chhatrapati Shivaji College, Omerga-413606, Maharashtra, India)
Abstract: Dirac-Maxwell’s equations, retained for magnetic monopoles, are generalized by introducing
magnetic scale field. It allows the magnetic monopoles to be time-dependent and the potentials to be Lorentz
gauge free. The non-conserved part or the time-dependent part of the magnetic charge density is responsible to
produce the magnetic scalar field which further contributes to the magnetic and electric vector fields. This
contribution makes possible to create an ideal square wave magnetic field from an exponentially rising and
decaying magnetic charge.
Keywords: Dirac-Maxwell’s equations, Lorentz Gauge, Magnetic scalar field
I. INTRODUCTION
The Maxwell–Heaviside equations prescribe both open dissipative systems having coefficient of
performance (COP) > 1 and equilibrium systems having COP < 1. Imposition of the Lorentz symmetrical
regauging reduces the set of Maxwell–Heaviside equations into a subset which discards open dissipative
Maxwellian systems and retains only those in equilibrium [1]. However, the discarded class of Maxwellian
systems contains all Maxwellian electromagnetic (EM) power systems exhibiting COP > 1, by functioning as
open dissipative systems freely receiving and using excess energy from the active vacuum. To study the open
dissipative systems the potentials are to be made Lorentz gauge free. While studying such systems,
Anastasovski et al [2] obtained equations for vacuum current density and vacuum charge density and proposed
to pick up by a receiver and use to generate huge electrical energy. Similar results have been deduced by
Lehnert [3–6] and Lehnert and Scheffel [7] from the condition of a nonzero charge density from vacuum
fluctuations in combination with the requirement of Lorentz invariance. By another approach Teli and Jadhav
[8] removed the Lorentz condiction on potentials by introducing scalar potentials in the Generalized Dirac-
Maxwell’s equations which made the electrical charges time varying in nature. These charges then did not
satisfy the continuity equation. The non-conserved part of the charge density was accommodated in terms of a
scalar field. They obtained electromagnetic fields of non-conserving electric charged particle. However,
magnetic monopoles, elementary particles with a net magnetic charge, have been a curiosity for physicists and
many believe they ought to exist. Our attempt is to find out the fields of non-conserving magnetic monopoles
with removing Lorentz gauge on the potentials.
The next section includes the Generalization Maxwell’s equations for magnetic monopoles by
introducing a magnetic scalar field H0, which removes the Lorentz condition on the potentials. In section 3, the
magnetic scalar field, in addition to the magnetic vector field and the electric vector field of a time-dependent
magnetic monopole is obtained. It is found that the magnetic scalar field H0 is a function of the time rate of
change of the magnetic charge on the monopole. In section 4, the magnetic vector field and magnetic scalar field
of a stationary time-dependent magnetic monopole are evaluated. Section 5 includes calculation of ideal square
wave magnetic field from a rising and decaying magnetic monopole. Section 6 includes the discussion.
II. GENERALIZATION OF MAXWELL’S EQUATIONS FOR MAGNETIC MONOPOLES
Analogous to [8], we may introduce a scalar function H0 into Dirac-Maxwell’s equations retained for
magnetic monopoles only to accommodate the time dependent part of the source densities such as
0 E (1a)
m
ρHP 401 H (1b)
m
c
HP
tc
j
H
E
41
02
(1c)
0
1
tc
E
H (1d)
where P1 and P2 are operators and H0 is a magnetic scalar field.
As usual the vector fields can be expressed in terms of the potentials
2. Electromagnetic fields of time-dependent magnetic monopole
www.iosrjournals.org 56 | Page
m
AE (2a)
t
A
c
m
m
1
H (2b)
These potentials satisfy the usual differential equations:
m
m
m
tc
4
1
2
2
2
2
(3a)
m
m
m
ctc
j
A
A
41
2
2
2
2
(3a)
provided that
tctc
HP
m
m
11
01 A (4a)
tc
HP
m
m
1
02 A (4b)
These equations give
tc
H
m
m
1
0 A (5)
with
tc
P
1
1 , 2P (6)
The magnetic scalar field H0 is the actual replacement of the Lorentz condition. If the potentials satisfy
the Lorentz condition, the magnetic scalar field disappears and the Dirac-Maxwell’s equations for magnetic
monopoles attain their original form. The generalized Dirac-Maxwell’s equations for magnetic monopoles are
then:
0 E (7a)
m
ρ
t
H
c
4
1 0
H (7b)
m
c
H
tc
j
H
E
41
0
(7c)
0
1
tc
E
H (7d)
Equations (2a), (2b) and (5) are solutions of Generalized Dirac-Maxwell’s equations.
m
ctc
jE
41
2
2
2
2
(8a)
tc
c
ctc
m
m j
H
141
2
2
2
2
(8b)
tcc
H
tc
m
m 141
02
2
2
2
j (8c)
In the absence of the sources, all of them propagate with velocity c in vacuum. Equation (8c) shows
that the charges satisfy the continuity equation in the absence of the scalar field.
III. FIELDS OF A TIME-DEPENDENT MAGNETIC MONOPOLE
For a time-dependent point magnetic monopole, the equations (3) have usual solutions as given by
Panofsky and Philip [9]:
S
'tq
t,r
m
m
(9a)
S
't'tq
t,r
m
m v
A (9b)
3. Electromagnetic fields of time-dependent magnetic monopole
www.iosrjournals.org 57 | Page
where
c
RS
vR
, r'rR , r is the field point vector, r' is the source point vector at the retarded time 't
defined by c/Rt't and v is the instantaneous velocity of the monopole.
The EM fields for such a monopole in arbitrary motion, using equations (2), (5) and (9), are
233
2
0 1
cS
'dt
d
c
r
S
c
r
q
S
c
r
H
m
vv
rr
v
r
v
r
H
(10a)
233
2
0 1
crS
'dt
d
c
r
cS
q
cS
H m
vv
rrr
rvrv
E
(10b)
'dt
dq
cS
H
m
1
0 (10c)
Both the fields H and E receive contributions from the instantaneous value of the magnetic charge on
the monopole as well as the rate of the change of the charge with time. Clearly, the magnetic scalar field H0 is a
function of the rate of change of the magnetic charge on the monopole with time. For time-independent
magnetic charge on the monopole, the scalar field disappears and the above field equations reduce to their usual
forms.
IV. MAGNETIC FIELD OF A STATIONARY MAGNETIC MONOPOLE WHOSE CHARGE IS
CHANGING WITH TIME
The net magnetic field due to a magnetic monopole when its velocity is zero, using equation (10a) and
with dt'dt , is
dt
dq
c
r
q
r
r
m
m
2
n
H (11a)
0E (11b)
and
dt
dq
cr
H
m
1
0 (11c)
Thus it is possible that H vanishes at 0rr , if
00
dt
dq
c
r
q
m
m
(12)
which gives
dt/dq
cq
r
m
m
0 (13)
Thus, if 0r to be positive, dt/dqm
should be negative, i.e. the magnetic charge should decrease with time.
For decaying magnetic charge on the monopole, equation (11) with respect of equation (13) gives
0
2
1
r
r
r
q
r
m
n
H (14)
It suggests that, if the magnetic charge on the monopole is positive and decaying, then at 0rr , H is
zero, for 0rr , H is positive, and at 0rr , H is negative, where 0r is given by equation (13).
V. IDEAL SQUARE WAVE MAGNETIC FIELD FROM A RISING AND DECAYING MAGNETIC MONOPOLE
Developing an ideal square wave magnetic field at any point in space from conserved magnetic
monopoles is impossible. But if the charge on the magnetic monopole is not conserved then the property of
vanishing field from a decaying magnetic charge and maximum saturation value from an exponentially rising
charge makes it possible to construct an ideal square wave magnetic vector field.
4. Electromagnetic fields of time-dependent magnetic monopole
www.iosrjournals.org 58 | Page
Suppose that a charge m
q is initially at m
q1 and it rises to m
q2 in time T according to the following
equation
m/tmm
qeqq 10 1
for Tt 0 (15)
At t = T, it reaches a maximum value m
q 2 given by
m/Tmm
qeqq 102 1
(16)
The field produced in this time interval is
2
1
2
0
11
r
q
e
c
r
r
q m
/t
m
nn
H
(17)
Thus the magnetic field at cr is independent on the instantaneous value of the magnetic charge on
the monopole.
In the further time interval T to 2T, suppose, the charge decays exponentially according to the equation
/tTmm
eqq
2 for TtT 2 (18)
The field produced in this time interval as computed from (11) is
c
r
r
eq /tTm
1
2
2n
H (19)
Thus the field at cr is zero and is again independent on the instantaneous value of the magnetic
charge on the monopole.
The requirement of Tqq mm
20 gives
/Tmm
eqq
21 (20)
Equations (19) and (23) give mm
qq 02 .
We thus see that for the decaying interval the magnetic field at cr , by equation (19), is zero, while
during the charging interval the field at cr , by equation (17), is
const
mm
r
qq
H
n
H
2
10 (21)
Thus periodically the field H attains only two states at cr viz. 0 and constH , which is an ideal
square wave magnetic field.
VI. DISCUSSION
Dirac-Maxwell’s theory under the Lorentz gauge does not include a time-dependent term of the
magnetic charge in the fields. To see the effect of the time-dependence of magnetic charges on their fields,
Dirac-Maxwell’s equations are made Lorentz gauge free. It shows the contribution of the rate of change of
charge with time to the fields. Outcome of this proposition is that two magnetic charges of the same type can
attract each other if they are decaying with time then
dt
dqm
is negative for both and are placed apart by the
distance
dt/dq
cq
r
m
m
(equation (11)), where m
q is the instantaneous value of both the charges, since beyond
the distance
dt/dq
cq
m
m
the field gets inverted. It is clear that if the magnetic charges are time-independent then
the scalar field H0 disappears and the generalized Dirac-Maxwell’s equations reduce to their usual form.
REFERENCES
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