Chapter 3: Electromagnetic Interaction

by Austin Cole, Josefine Fabricius and Andrea Lavilles

Charles Augustin de Coulomb & Coulombs Law of Electrostatics

Born on June 14, 1736, Charles Augistin de Coulomb was a French phycisist from a wealthy family. He grew up in Angouleme, France, and took a particular liking to studying mathematics. He began working at his father’s business in Montpellier, but later joined military school, which eventually lead to his participation of the construction of a fort in Martinique, a French colony in the Caribbean. Upon his return to France, Coulomb discovered the inverse relationship of the force between electric charges and the square of its distance. This came to be known as Coulomb’s Law. Coulomb died in Paris on August 23, 1806.
First published in 1785, Coulomb’s law, or Coulomb’s inverse-square law, was key to the development of the theory of electromagnetism. The law describes the electrostatic interaction between electrically charged particles. It states that, “The magnitude of the Electrostatics force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of charges and inversely proportional to the square of the distances between them." To calculate this force, this equation is used: F = ke (q1q2/r^2) , where r is the distance between the point charges and ke is a proportionality constant. The unit of measurement of this force F is the Coulomb C, or charge transported by a steady current of one ampere in one second. It is the SI unit of electrical charge.

Hans Christian Oersted & Oersted's Discovery

Hans Christian Oersted was born in 1777 on Rudkjobing in Denmark (NNDB). He studied to be a doctor in philosophy in 1799 and gave lectures in chemistry and natural philosophy. Oersted was first to identify the relationship between electric currents and magnetism. In 1820 his discovery that sending an electric current through a wire created a magnetic field was published.
Scientists and even the ancient Greeks were aware of iron magnets and lodestones, naturally made magnets with iron cores (Bellis). It was Oersted that found an alternative method of magnetism. Oersted set up a demonstration for his friends and colleagues by heating up a wire by using an electric current and he also had a compass on hand for magnetism demonstrations. During the electricity demonstrations he noticed that the compass needle moved when the electric current was switched on and off. The needle was not attracted or repelled by the wire but instead stood at right angles from it. Oersted contemplated his discovery but did not publish any explanation for his findings. Oersted’s discovery is vital to modern society because it shows that using a changing magnetic field can generate electricity; and that electricity can generate a magnetic field (Than). The implications of this discovery can be found in MRI machines to engines.

Felix Savart

Felix Savart was born June 30, 1791 in Mezieres, France. His family had a history of becoming engineers and being involved in the military, but Savart chose a different route and chose to study medicine instead. France at this point was enjoying the victories from the rule of Napoleon, and after a few years of training Savart was drafted to become a surgeon for the army. After several of Napoleon�s defeats, Savart was discharged from the army and continued his medical education. After graduating with a degree in medicine in Strasbourg, Savart focused on getting more medical experience and translating De Medicina by Aulus Cornelius Celsus.
In Metz, Savart set up a medical practice but found he spent more time working on physics than treating patients. He then built a physics laboratory in which he studied sound, and in particular, tried building violins according to mathematical principles. In 1819, Savart went to Paris to find a publisher for his translated De Medicina and so he could speak to Biot about the acoustics of instruments. Biot found Savart�s findings interesting and Savart even created and demonstrated a trapezoidal violin that provided a superior sound to the normal violin.

Biot was also studying electricity when Savart arrived, which led to the pair joining up when they heard of Hans Christian�s Oersted�s discovery that when a compass needle that was near a wire with a current going through it pointed at right angles to it. Together they discovered the Biot-Savart law: magnetic fields produced by electric currents can be calculated using the law. They published the paper "Note sur le magnetisme de la pile de Volta" in 1820.
Savart began teaching science in a private school in 1820 and later was elected to the Academy of Sciences and became a professor of experimental physics. Savart published some works on his experiments with sound by revealing some of the science on the vibration of the instrument and other objects that are brought into its vicinity. He also created the Savart disk which was a rotating disk that helped determine the tone of an instrument by matching the tone. The frequency was easily determined by the Savart disk. He used his technology to help study harmonious and discordant sounds.
Savart passed away in Paris on March 16, 1841 a few months short of his 50th birthday.

Michael Faraday & Faraday's Law of Induction

Born on September 22, 1791, Michael Faraday was an English chemist and physicist who made many important contributions to science despite his lack of formal education in mathematics. His research with magnetic fields around conductors carrying DC electric currents lead to the basics of the electromagnetic field in physics, which was later further researched by James Maxwell. Faraday established that magnetism could affect rays of light, discovered the principle of electromagnetic induction, diamagnetism, and the laws of electrolysis, invented electromagnetic
rotary devices which formed the foundation of electric motor technology, helped make electricity viable for use in technology, discovered benzene, investigated the clathrate hydrate of chlorine, invented an early form of the Bunsen burner and the system of oxidation numbers, and popularised terminology such as anode, cathode, electrode, and ion.

Faraday’s law of induction is a basic law of electromagnetism relating to the operating principles of transformers, inductors, and many types of electrical motors and generators. It states that, “The induced electromotive force (EMF) in any closed circuit is equal to the time rate of change of the magnetic flux through the circuit.” It only applies to closed circuits made of thin wire. The unit of capacitance called the farad F was named after Faraday. A farad is the charge in coulombs which a capacitor will accept for the potential across it to change 1 volt.

James Clerk Maxwell

James Clerk Maxwell was born on June 13, 1831 in Edinburgh. His father was a lawyer and came from a well-off family. He grew up in the Scotland countryside as an only child. MaxwellÂ’s mother educated him for the first few years of his life, but she died of cancer when Maxwell was only eight years old. MaxwellÂ’s father hired a tutor for him to begin his formal education. In 1841, after two years of tutoring, MaxwellÂ’s father decided to dismiss the tutor and send James to Edinburgh Academy. He had to start in the second year, meaning that everyone in his class was a year older than him. Maxwell was picked on by his classmates because of his country mannerisms and accent. While at the academy, Maxwell won awards in math and English and wrote his first scientific paper, Oval Curves. The paper was presented to
the Royal Society of Edinburgh. Maxwell was only fourteen and was considered too young to present the work, so it was instead presented by James Forbes, a professor at Edinburgh University.

Maxwell finished his schooling at the academy when he was sixteen years old. He continued his education at the University of Edinburgh. During his studies, he performed many experiments on his own using equipment he made. These experiments were mostly focused on the properties of light. Maxwell wrote two more papers while an undergraduate, but he was once again deemed too young to present his own papers. After his time at Edinburgh University, Maxwell went to Cambridge University to earn a graduate degree. He studied there from 1851 until he graduated in 1854 with a mathematics degree. Maxwell decided to apply for a fellowship, which was granted late in 1855. The next year, however, Maxwell was encouraged by his former professor Forbes to apply for a vacant position at Marischal College. Maxwell was accepted for the position and left Cambridge at the end of 1856.

While the professor of Natural Philosophy at Marischal, Maxwell continued his studies in mathematics, optics, and physics. He solved the mystery of how SaturnÂ’s rings remained stable by proving mathematically that they were made up of many small particles. Maxwell also met Katherine Dewar while he was at Marischal and went on to marry her in 1859. In 1860, Maxwell left Marischal College and became a professor at KingÂ’s College in London. During his time there, Maxwell made many advances in the study of electricity and magnetism. Maxwell taught at KingÂ’s College until 1865, when he resigned and returned to the house where he grew up.

Maxwell continued writing while he was not teaching. In 1871, Maxwell returned to Cambridge as a professor of physics. James Maxwell died on November 5, 1879, from the same type of abdominal cancer that his mother suffered from. Many of his unpublished works were printed after his death by Cambridge University.

Maxwell's Equations>
James Maxwell’s 1861 paper titled “On Physical Lines of Force” took all of the current knowledge of electricity and magnetism and reduced them into a set of differential equations. There were twenty of these equations and a total of twenty variables. Maxwell used these equations to calculate the propagation speed of an electromagnetic field, which was approximately the speed of light. From these calculations, Maxwell concluded that light is an electromagnetic disturbance and follows the same laws.
Maxwell reduced his set of equations into four partial differential equations. There are two variants of Maxwell’s equations, a “microscopic” set and a “macroscopic” set. The “microscopic” set, also known as Maxwell’s equations in a vacuum, use the total charge and total current present. The “macroscopic” set, or Maxwell’s equations in matter, are only dependent on depend only on free charge and free current. In addition, Maxwell’s equations can be written in both an integral and a differential form.
The first of Maxwell’s equations is also known as Gauss’s law. It describes the relationship between electrical charges and the electric field that they produce. The second is known as Gauss’s law for magnetism. This equation describes the existence of magnetic fields and magnetic flux. All magnets exist as dipoles, meaning that each magnet has both a north and south pole. There are no magnetic monopoles that have only a north or south pole. The third of Maxwell’s equations is known as Faraday’s law. It states that a magnetic field that changes can create an electric field. The final of Maxwell’s equations is a variant of Ampere’s law. This corrected equation describes the two ways a magnetic field can be created. One way is by an electrical current, and the second is by a changing electric field.

Magnetic force (velocity dependence)

The magnetic force is a force that acts on a charge moving through a magnetic field. This moving charge can take the form of either a current in a wire or a charged particle moving with some velocity. The magnitude of this force is proportional to the current and the magnitude of the magnetic field, and the direction of the force is perpendicular both to the magnetic field and to the direction of the current. Additionally, magnetic fields can be produced by moving charges. This means that two current carrying wires placed side by side will each experience a magnetic force caused by the magnetic field of the opposite wire. It is important to note that a charge object will only feel a magnetic force if it is moving.

Heinrich Hertz

Heinrich Hertz was a German physicist born in 1857 in Hamburg. His family was quite prosperous, so he had access to high quality education. Hertz was particularly skilled in science and engineering. He studied at many schools across Germany, earning his PhD in 1880 from the University of Berlin. After earning his degree, Hertz did some post-doctoral study and eventually took a professorship at the
University of Karlsruhe. Hertz made many contributions to the study of electromagnetic theory, expanding the ideas that had been put forward by James Maxwell. In 1886, Hertz was able to prove the existence of electromagnetic waves. He did so by setting up a radio wave transmitter that produced a spark at a set frequency. He then used a circle of wire with a very small gap between the ends as a receiver. The electromagnetic waves produced by the transmitter created an oscillating current in the loop of wire which created sparks across the gap in the receiver. Hertz was able to refine his experiments to show that these electromagnetic waves travelled at the same speed as light, thereby proving Maxwell’s hypothesis. For his contributions, the unit for frequency was named the “hertz.”