History of Maxwell Equations | Maxwell biography | History of Electromagnetism | James Clerk Maxwell

The history of electromagnetic theory begins with ancient measures to understand atmospheric electricity, in particular lightning. During that time, people had little understanding of electricity and were unable to explain the phenomena. At the dawn of 18th and 19th century, philosophical and religious ideas led many scientists to accept the argument that seemingly separate forces, for example electricity, magnetism, light, shared a common and fundamental source. In addition to a search for a common source of all natural phenomena, an elusive ether through which light could pass was thought necessary to explain the wave-like behavior of light. In the 19th century, it had become clear that electricity and magnetism were related and their theories were unified. Wherever charges are in motion, electric current results and magnetism is due to electric current. The source for electric field is electric charge, whereas that for magnetic field is electric current charges in motion. Scientific understanding into the nature of electricity grew throughout the 18th and 19th centuries through the work of researchers such as Coulomb, Ampere, Faraday and Maxwell. Born in France and baptized at the parish church of Saint-André, Charles-Augustin de Coulomb studied philosophy, language and literature. When his father suffered a financial setback, he was forced to leave Paris and went to Montepelier where he submitted his first publication to the Society of Sciences in Montepelier. He graduated in 1761 and joined the French army as an engineer in the rank of a lieutenant. Over the next 20 years, he was posted to a variety of locations where he was involved in engineering, structural fortifications, soil mechanics as well as other fields of engineering. Coulomb's law which you can see at the right hand side corner of the screen or Coulomb's inverse square law is an experimental law of physics that quantifies the amount of force between two stationary electrically charged particles. The electric force between charged bodies at rest is conventionally called electrostatic force or Coulomb force. Although the law was known earlier, it was first published in 1785 by him, hence the name Coulomb's law was essentially to the development of the theory of electromagnetism and maybe even it is considered as a starting point as it made to possibly to discuss the quantity of electric charge in a meaningful way. Andre Marie Ampère was born into a well-to-do family in the city of Lyon, France on January 20, 1775. His father was Jean-Jean Ampère, a businessman. The education of Andre Marie received was rather unusual. His father was a great admirer of Jean-Jean Rousseau, one of the leaders of the French Enlightenment. He decided to follow Rousseau's approach for Andre Marie's education. This meant no formal lessons although as a child of the French Enlightenment, Andre Marie did not reject the church and remained a practicing Catholic throughout his life. At the age of 13, Andre Marie began a serious study of mathematics using books in his father's library. He submitted a paper about conic sections to the Academy of Lyon but was rejected. Ampère began by repeating Ørsted's work and before the end of this September 1820, he made his own discovery. He found that if electric current flows in the same direction in two nearby parallel wires, the wires attract one another. If electric current flows in opposite direction, the wires repel to one another. Ampère had discovered something amazing. He had produced magnetic attraction repulsion in the complete absence of any magnets. All of the magnetism was generated electrically. He called this new phenomena field of electrodynamics. Ampère then brilliantly found an equation which is right there on your screen, an equation connecting the size of magnetic field to the electric current that produces it. The story of Michael Faraday's life is one of the most romantic stories in the annals of science. It will continue to inspire in countless ways. Faraday rose from a bookbinder's apprentice to become one of the greatest scientists of all time. He is acknowledged as one of the greatest thinkers of his time. He was a true pioneer of scientific discoveries. His discoveries have had a spectacular effect on successive scientific and technological developments. Faraday attended a day school and received only the basic education to read, write and count, that is the traditional three hours, reading, writing and arithmetic. Given his family background, nothing much could be expected. The Faraday's were desperately poor. When Faraday was 13 years old, he had to find work to help the family finances. Faraday learned the trade of bookbinding as well as it is evident that in later years he bound many volumes for himself and many of them are still in existence. He was a great builder of instruments. Faraday was a great popularizer of science. He initiated popular science lectures for children and general audiences at the royal institution. Faraday's law of induction is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force abbreviated as EMF, a phenomena known as electromagnetic induction. It is the fundamental operating principle of transformers, inductors and many types of electrical motors, generators and solenoids. The time that we are talking about was then when scientists understood very little about the concepts and ideas like electricity and magnetism. Truth to be told, they knew even less about the relationship between the two but they were starting to study, explore, experiment, dig So to speak into the mystery of the universe, German physicist Heinrich Lenz made an enduring contribution I would say to physics. Lenz's law and in doing so he made his mark on magnetic history. Lenz was born actually in Estonia. He studied chemistry and physics both at a local university and traveled with famous navigator who was on his third world expedition. It was during his expedition that Lenz began to study the physical properties of seawater or salt water and other climatic conditions. Post voyage he began to work in St. Petersburg, Russia, later serving as a dean of mathematics and physics and a senior official in academics. He also started studying, you guessed it right, yes it is electromagnetism. Lenz's law which is there on your screen at the right hand side button says that the introduction of a conductor within an electromagnetic field will produce an electricity inducing an opposite field that repels the magnetic fields producing the charge. It is basically a consequence and the converse conservation of energy. According to this law the total energy in the universe must remain constant. If the field that is associated with the current moves in the same direction as the charge in the magnetic field that created, the two fields would combine and create a net field that would induce a current with double the magnitude. But there was a problem. The problem was that all these equations which you can see on your screen are concepts I would say which were scattered. The concepts of electricity at one hand and magnetism on the other hand were seemingly same concepts which looked to emerge at one place but was unable to find its way home. The wildness of thought, the disparity of ideas seemed to kindle the idea of unification. The two concurrent forces of nature appeared to be generated from the same source yet the source dispersed into the uncharted waters which appeared as a mirage in front of physicists who were finding it difficult to grab the central idea. In 1819, 12 years before Maxwell was born, the field of electromagnetism was born. Hans Christian Oersted of Denmark had suspected that electricity and magnetism were related in some way for some time and was finally able to create some evidence for it. So you see on the screen a suspected electricity and magnetism were related. The first connection between electricity and magnetism was established. What he did was that he held a wire above the compass and the compass needle was deflected by nearby electric current. So when a current traveled through the wire, he noticed that the needle of the compass moved. For this discovery, the Royal Society of London awarded Oersted the Copley Medal in 1820 and the French Academy granted him 3,000 francs. Oersted's findings stirred much research into electrodynamics throughout the scientific community influencing French physicist André-Marie Ampère's developments of a single mathematical formula to represent the magnetic forces between current-carrying conductors. Oersted's work also represented a major step forward, a unified concept of energy. The picture that you see on your screen is what is called a galvanometer, an electromechanical measuring instrument for electric current. A galvanometer works by deflecting a pointer in response to an electric current flowing through a coil in a constant magnetic field. Based on Oersted's experiments that a magnet's compass needle deflects when near a wire which have electric current, Johann Schweiger at the University of Hale on 16 September 1820 designed what is called the first world's first galvanometer. Schweiger was born in Erlanger, Bavaria, Germany on 8 April 1779. He was educated at the University of Erlanger where he received his PhD degree in 1800. He used Oersted's discovery of electromagnetism for his invention. Schweiger developed the galvanometer as a tool for measuring the strength and direction of electric current. Schweiger, however, became one of the first scientists after Oersted's discovery to demonstrate a determination and an interest in experimentation of electromagnetism. As co-editor of the Journal for Chemistry and Physics, he probably read Oersted's manuscript submitted to the Journal for Review and Publication. Schweiger then attempted through experimentation like Oersted the construction of large piles to improve the performance of electromagnetism. John Clerk, later Clerk Maxwell, a Midby of Midby, was a Scottish advocate and father of the famous physicist James Clerk Maxwell. He was born in Edinburgh on 10 November 1790, the son of Janet Irving and Captain James Clerk. He studied law and qualified as an advocate in 1811. He inherited the Middleby estate in the Dumfriesshire from his mother Dorothea Clerk. Maxwell, upon her death in 1793, assumed the additional surname of Maxwell. He was elected a fellow of the Royal Society of Edinburgh in 1821, his proposer being Sir George Stuart McKenzie. In the 1830s, he is recorded as living at 14 India Street in Edinburgh's second new town, which is where James Clerk Maxwell was born. He married Frances Hodgson Kay, daughter of Robert Hodgson Kay and Elizabeth Liddell. Their children included the mathematical physicist James Clerk Maxwell. James Clerk Maxwell was born on 13 June 1831 at 14 India Street at Edinburgh of Middleby, an advocate and Frances Kay's daughter of Robert Hodgson Kay and sister of John Kay. His father was a man of comfortable means. Recognizing the boy's potential, Maxwell's mother Frances took responsibility for his early education, which in the Victorian era was largely the job of the woman of the house. At eight, he could recite long passages of Milton and the whole of the 119th poem. Maxwell was fascinated by geometry at an early age, rediscovering the regular polyhedra before he received any formal instruction. At the age of 18, Maxwell contributed two papers for the transactions of the Royal Society of Edinburgh. One of these on the equilibrium of elastic solids laid the foundation for an important discovery later in his life, which was temporarily double refraction produced in viscous liquids by shear stress. In October 1850, already an accomplished mathematician, Maxwell left Scotland for the University of Cambridge. In 1854, Maxwell graduated from Trinity with a degree in mathematics. He scored second highest in the final examination, coming behind Edward Routh and earned himself the title of second wrangler. Maxwell's times at King's was probably the most productive of his career. He was awarded a Royal Society Rumford medal in 1860. This period of life would see him display the world's first light fast colour photograph, further develop his ideas on the viscosity of gases and propose a system of defining physical quantities now known as dimensional analysis. Maxwell would often attend lectures at the Royal Institution where he became into regular contact with Michael Faraday. The relationship between the two men could not be described as being close because Faraday was 40 years Maxwell's senior and showed signs of senility. They nevertheless maintained a strong respect of each other's talents. Now here is something interesting which I would like to draw your attention. At the International Science Festival in Edinburgh in 1991, there was a unique meeting when there came together two members of the present generation who were related to James Clerk Maxwell and his lifelong friend and scientific colleague Peter Guthrie and Tate, Professor of Natural Philosophy at the University of Edinburgh for over 40 years. Present was Sir John Clerk, 10th Baronet and great grandson of Maxwell's uncle Sir George Clerk and Mr Tate, a great grandson of Professor P.G. Tate. It was probably over a hundred years since the Clerks and Tates had last met, a reminder of a unique era in Scottish intellectual life. Right on your screen you can see his father's side. All were great geniuses. James Clerk Maxwell came from a remarkable line of progenitors. You see here he seemed to exemplify the relationship of his towering intellect to genetic inheritance. The famous concert pianist John Lell after winning the International Tchaikovsky Piano Competition in Moscow was asked where had he got his music from. So he was somehow perplexed by this question and unable to answer it since none of the previous generations of his family had been at all musical. If James Clerk Maxwell had been asked a similar question he would not have to had to look very far for an answer. On his father's side right here on the screen he was a member of the Clerk family, the Clerks of Penicuik and on mother's side a member of the Clay family, the Cays of Northumberland. So you can see that this his family lineage is very rich and you can see from his father's side and his father's side all were great people. The first paper that James Maxwell published after earning his graduate degree was a 75 page analysis of what is called Faraday's concept of lines of forces. Now published in 1855 and was suitably titled on Faraday's lines of force. Now Maxwell translated Faraday's ideas into mathematics. Maxwell created something which is right on your which is called you know vectors right to describe the main players of electromagnetism. So you can see here E the electric field of intensity, H the magnetic field of intensity, B the magnetic flux of intensity and I the electric current. E and H are forces and B and I are fluxes which we will soon come to know and a way to picture flux is there on the screen is to imagine having a square loop of a wire or a flow of river. The flux of the velocity of the water would be considering how much water will flow through the loop. The flux of an electric field is proportional to the number of electric field lines that would go through that. On 16th of June 1865 James Clerk Maxwell's paper, electromagnetic I would say let us look into this paper once more. Yeah so it says a dynamical theory of the electromagnetic field was said to the printers Taylor and Francis for publication in philosophical transactions of the Royal Society. Now here is something quite amazing. Now six days earlier on 10th of June of the same year Richard Wagner, Streisand and Slode had its world premiere in the court theatre of Munich. The world revolutionary is the only adjective which begins to do justice to the extraordinary impact of these two events of 1865. One in the physical sciences and other in music, opera and drama. Wagner's staggering innovations in musical harmony, structure and dramaturgy revolutionized the approaches of composers and profoundly influenced the music of the late 19th and 20th centuries. Music would never be the same again. On the right hand side you see the gentleman Maxwell's monumental paper laid the foundation for the innovations of the 20th century. Physics by placing fields at the heart of the theory of electromagnetism and all of the subsequent fields which describe how matter and radiation behave at a fundamental level. So this is quite an unusual analogy. Richard Wagner with his great opera Tristan and Slode and James Clerk Maxwell with his theory of electromagnetism. I just tried to show it because these two are both revolutionaries and each other aspect. So in 1865 when Wagner supported this on the 10th of June on the same year so it revolutionized both music as well as what we call the theory of electromagnetism. Now what I would like to show you here is that these are the original Maxwell's 20 equations. So you see here so this one is named as B on the right hand side. These are the three equations of magnetic force, three equations of electric currents and three equations of electromotive force. Mind it that these are original Maxwell's equation not the reduced one which we studied today. Going further what we see is this. We find the three equations of electric elasticity, three equations of electric resistance and three equations of total currents and further what we find is this one equation of electricity and one equation of continuity. Now if you add them all together 1 plus 1 2 and the earlier one it comes to 10 right. So what I have done is that these are the reduced to 8 equations which you can see earlier where the original 10 equations and this thing obviously is taken from a website so I feel happy to quote and bring before you the Royal Society publishing right there in front of the screen. I've mentioned where from I have taken along with the DOI number of the research paper and the Royal Society website so that there is no confusion in the video. These are the 10 equations original 10 equations and these are the reduced 8 equations which we find. So this is kind of an historical context. So these are the reduced to 8 equations right as you can find it. Now although Maxwell's most important equations has already appeared through his seminal paper entitled on physical lines of force which was written in around 1861. It was not until 1865. Now this is the paper as you see on the left hand this is the on physical science 1861 but it was not until 1865 that Maxwell created a distinct listing of 8 equations in his follow-up paper known as this one a dynamical theory of the electromagnetic field. This was in a section headed as general equations of the electromagnetic field while Maxwell refers to 20 equations at the end of the section. However there in fact only 10 equations which I have just shown you. Maxwell arrives at the figure of 20 because he splits six of these equations into three cartesian components. Now Maxwell's original eight equations if I see are this. The first one the displacement current the total electric current is the sum of the conduction current and the displacement current. The second one marked in red in a box the flywheel equation appeared as the 55th equation in part 2 of the original 1861 paper which is on the left hand side and it exposes the fine-grained rotational nature of the magnetic field. Maxwell identified faraday's electrotonic state with a vector a which he called the electromagnetic momentum. The vector a relates to the magnetic intensity h through the curl equation. Coming to the third Maxwell's third equation is derived hydrodynamically and it appears as Ampere's circuital law. Coming to the fourth marked here in a box of red colored originally appeared as equation 77th in part 2 of his 1861 paper and it takes this form. Coming to the fifth one this is the elasticity dielectric constant and permittivity. Maxwell's fifth equation is the equation of electric elasticity which first appeared in the preamble of part 3 of his 1861 paper and then again in at an equation 105 in the same part. In 1864 the negative sign was removed and it appeared in this form. The sixth paper which is this one Maxwell's sixth equation is the ohm's law. Coming to the seventh equation which is this right at the bottom of your screen this appeared as 115th in his 1861 paper is the gauss's law and the last equation which is right there at the bottom is Maxwell's eighth equation number 113 in his 1861 paper which is called the equation of continuity. So this gives you a total idea of the original 1861 paper the numbers and the earlier the 10 you know i would say the 10 equations and how it has been reduced to 8 equations. The self-taught mathematician so okay so this is the original equations again i have taken from a researcher called Frederick David Thome. Here is the i have taken it from research gate so here is the url and if you wish you can go there. Now the figure of the person standing on your left hand side of the screen is a self-taught mathematician and physicist Oliver Heaviside's parents were Rachel Elizabeth West and Thomas Heaviside. He was born on May 1815. Oliver the youngest of his parents four sons and he was born at 55 king street in cammon town. He caught scarlet fever when he was a young child and this affected his hearing. This was to have a major impact on his life making his childhood unhappy with relations between himself and other child difficult. Now in 1884 he recasted Maxwell's mathematical analysis from its original converser form to the modern vector terminology. It reduced the equations down to four differential equations in two unknowns as we know as Maxwell's equations. The four reformulated equations describe the charges magnetic fields and the relationship between two. So the first equation right there on your screen relates electric flux to the volumetric change density. The second equation says which is right on your screen that a magnetic field does not diverge because there are no monopoles. The third equation summarizes the result from faraday's electromagnetic induction. The voltage induced in a circuit was proportional to the time rate of change of magnetic flux through the circuit and the fourth is from Ampere's law. The magnetic field in a closed loop around the current was in fact equal to the current through the loop. So these are the four reduced form which was done by Heaviside. Now this is the Gauss's law of electricity, Gauss's law of magnetism, Faraday's law of induction and Ampere's law which has both differential and integral form. I'm so sorry this is coming up in the next part of my video. Now a treatise on electricity and magnetism, this is a two-volume treatise on electromagnetism which was written by James Clerk Maxwell in 1873. Maxwell was revising the treatise for a second edition when he died in 1871. The revision was completed by William Davidson and was went for a publication in 1881. A third edition was prepared by J. J. Thomson and published in 1892. The treatise is said to be notoriously hard to read containing plenty of ideas which were lacking both in terms of clarity and orderliness which was allowed to catch on more easily. So you see the transformed electromagnetism in 12 equations. A means the vector potential, B the magnetic induction, C the electric current, D the displacement, E the electric field, I mean to say Maxwell's electromotive intensity, F is the mechanical force, H is the magnetic field and this is the magnetic force. So this is later published by James Clerk Maxwell in 1873. Now Maxwell's time at King's College London was probably the most productive in his career. He was awarded the Royal Society's Rumford Medal which I have spoken earlier in 1860 for his work on colour and was later elected on the society in 1861. This period of his life would see him display the world's first high-coloured photograph. Now he returned to Cambridge and became the first Cavendish professor of physics. Maxwell was put in charge with the development of the Cavendish laboratory, supervised at every step in the process of the building and the purchase of the collection of apparatus. As a great lover of Scottish poetry, Maxwell memorized poems and wrote his own, the best known is Rigid Body Sings, closely based on Coming Through the Rye by Robert Burns, which he apparently used to sing while accompanying himself on a guitar. In April 1879, Maxwell began to have difficulty in swallowing, the first symptom of his fatal illness. Maxwell died in Cambridge of abdominal cancer on 5th of November 1879 at the age of 48. His mother had died at the same age of the same type of cancer. Maxwell is buried at Parton Kirk near Castle Douglas in Galloway, close to where he grew up. As death approached Maxwell, he told to a Cambridge colleague, I have been thinking how very gently I have always been dealt with. I have never had a violent show all my life. The only desire which I can have is like David, to serve my own generation by the will of God and then fall asleep. Well, that is all a brief idea on James Cluck's Maxwell's life and the history of development of Maxwell's equations. In the next video, we would be talking about Maxwell's equations. We would deal with the detail on each and every aspect component and the mathematical part of Maxwell's equations. Do let me know your comment in the comment section. Don't forget to like, subscribe and let me know how the introduction to Maxwell's equation with a formidable history giving a clarity of idea from the development along with the historical part and followed by Maxwell's equations, the researchers and the death of Maxwell. How did you like it? So stay safe, stay happy and we all wish that this war gets over as early as possible. We have just ended with the pandemic and we really don't want again a war to rage around the world. Stay safe, stay happy and have a nice weekend ahead. Bye.