History of Maxwell’s Equation

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1 History of Maxwell’s Equation
Bambang Setia Nugroho

2 1785 Charles-Augustin de Coulomb reports that the force between two charges varies with the inverse square of the distance. Charles-Augustin de Coulomb

3 Johann Carl Friedrich Gauss

4 A Voltaic Pile, 1st DC battery Alessandro Volta
When a wire was connected to both ends of the pile, a steady current flowed. Volta found that different types of metal could change the amount of current produced, and that he could increase the current by adding disks to the stack. stack of alternating zinc and silver discs, separated by brine-soaked cloth. He built the pile, which consisted of as many as thirty disks A Voltaic Pile, 1st DC battery Alessandro Volta March 20, 1800 © , AMERICAN PHYSICAL SOCIETY APS encourages the redistribution of the materials included in this newspaper provided that attribution to the source is noted and the materials are not truncated or changed. Editor: Alan Chodos  Associate Editor: Jennifer Ouellette  Staff Writer: Ernie Tretkoff

5 Hans Christian Oersted
obtained the first evidence of a link between electricity and magnetism, During a lecture demonstration, on April 21, 1820, while setting up his apparatus, Oersted noticed that when he turned on an electric current by connecting the wire to both ends of the battery, a compass needle held nearby deflected away from magnetic north, where it normally pointed. On July 21, 1820, Oersted published his results in a pamphlet, which was circulated privately to physicists and scientific societies. His results were mainly qualitative, but the effect was clear–an electric current generates a magnetic force.  Hans Christian Oersted Editor: Alan Chodos  Staff Writer: Ernie Tretkoff Contributing Editor: Jennifer Ouellette  Science Writing Intern: Nadia Ramlagan

6 showed that two parallel current-carrying wires could be made to exhibit a mutual attraction or repulsion depending on the relative direction of the currents. by the early 1830s, Michael Faraday had shown that just as electricity could influence the behavior of a magnet, a magnet could affect electricity, when he showed that drawing a magnet through a loop of wire could generate current  André-Marie Ampère

7 Jean-Baptiste Biot, author of an acclaimed Treatise on Experimental and Mathematical Physics (Traité de physique expérimentale et mathématique), personally had experimented with Coulomb and was an ardent Newtonian. With Felix Savart, a physician fascinated by acoustics, Biot carried out very precise measurements to determine the force exerted by a conducting wire on the pole of a magnet and to deduce from these measurements a mathematical law for the action of a small slice of the conductor on this pole. Jean Baptiste Biot and Félix Savart 18 December 1820

8 Hendrik Lorentz

9 envisioned a mysterious, invisible “electrotonic state” surrounding the magnet—what we would today call a field.  He posited that changes in this electrotonic state are what cause electromagnetic phenomena. And Faraday hypothesized that light itself was an electromagnetic wave.  Michael Faraday Heinrich Friedrich Emil Lenz Lenz had begun studying electromagnetism in Besides the law named in his honor, Lenz also independently discovered Joule's law in 1842; to honor his efforts on the problem, it is also given the name the "Joule–Lenz law," named also for James Prescott Joule.

10 new physical concept: the displacement current
Displacement current isn’t really current. It’s a way of describing how the change in electric field passing through a particular area can give rise to a magnetic field, just as a current does. In Maxwell’s model, the displacement current arises when a change in electric field causes a momentary change in the position of the particles in the vortex medium. The movement of these particles generates a current. Maxwell completed the last key pieces of his electromagnetic theory in 1864, when he was 33  James Clerk Maxwell Focusing on the mathematics, he described how electricity and magnetism are linked and how, once properly generated, they move in concert to make an electromagnetic wave. 1855 Maxwell’s first paper on Faraday’s observations and theories debuts. 1861 & 1862 Maxwell publishes a four-part paper, “On Physical Lines of Force.” It introduces the core idea that a change in electric flux through a surface can create a magnetic field. 1864 Maxwell presents new work before the Royal Society of London, published the next year. It suggests that electric and magnetic fields can move through space in waves and that light itself is such a wave.

11 In the summer of 1884, Heaviside was investigating how energy moved from place to place in an electrical circuit. Is that energy, he wondered, carried by the current in a wire or in the electromagnetic field surrounding it? Heaviside ended up reproducing a result that had already been published by another British physicist, John Henry Poynting. But he kept pushing further, and in the process of working through the complicated vector calculus, he happened upon a way to reformulate Maxwell’s score of equations into the four we use today.  Oliver Heaviside One of the consequences of the work was that it exposed the beautiful symmetry in Maxwell’s equations. One of the four equations describes how a changing magnetic field creates an electric field (Faraday’s discovery), and another describes how a changing electric field creates a magnetic field (the famous displacement current, added by Maxwell). Oliver Heaviside publishes a condensed version of Maxwell’s equations, reducing the equation count from 20 to four John Henry Poynting

12 The equations can be written in different ways
The equations can be written in different ways. Here, J is the current density. E and B are the electric and magnetic fields, respectively. And there are two other fields, the displacement fieldD and the magnetic field H. These fields are related to E and B by constants that reflect the nature of the medium that the fields pass through (the values of these constants in vacuum can be combined to give the speed of light). The displacement field D was one of Maxwell’s key contributions, and the last equation describes how both current and changing electric fields can give rise to magnetic fields. The symbols at the beginning of each equation are differential operators. These compactly encode calculus that involves vectors, quantities that have a directionality and thus x, y, and zcomponents. Maxwell’s original formulation of his electromagnetic theory contained 20 equations. Four Golden Rules

13 1888 Hertz, several years after moving to a well-equipped laboratory in Karslruhe, reports confirmation of the existence of the electromagnetic waves predicted by Maxwell. Heinrich Hertz He noticed that something curious happened when he discharged a capacitor through a loop of wire. An identical loop a short distance away developed arcs across its unconnected terminals. Hertz recognized that the sparks in the unconnected loop were caused by the reception of electromagnetic waves that had been generated by the loop with the discharging capacitor. Radio Magic: Heinrich Hertz used the coil [left] and the antennas [right] to produce and detect electromagnetic radiation outside the visible range.

14 1940 Albert Einstein gives the term “Maxwell’s equations” a boost with his monograph “Considerations Concerning the Fundaments of Theoretical Physics.” Albert Einstein