![]() Ampère’s work elegantly combined experiments and theory. Ampère’s relentless scientific efforts over the next six years founded the field of electrodynamics, with at times fortnightly reports to the French Academy of Sciences and the publication of his general law connecting electric currents with magnetic forces. Soon after, Jean-Baptiste Biot and Philippe Savart showed the same forum how the strength of the force falls away with distance to the wire. News of Ørsted’s discovery spread quickly across Europe, and within a week Andre Ampère had shown the French Academy of Science in Paris that parallel currents in two wires attract each other, while opposite currents would repel. This changed in September 1820 while Hans Christian Ørsted was setting up a demonstration for a lecture in Copenhagen: he discovered that an electric current can deflect the magnetic needle of a compass. Up to this time, the laws of electricity and the laws of magnetism were regarded as two separate fields of physics. This law, and a similar one for magnets, was later generalized by the work of Poisson and Gauss in the early 19th century leading to Gauss’ Law, the physics behind the first of Maxwell’s Equations. The advances through the 18th century in understanding electric charges and currents, notably the work of Benjamin Franklin and Alessandro Volta culminated in the work of Charles Coulomb, whose law showed that the strength of electric force varied inversely with the square of the distance to a positively or negatively charged object. Here we will concentrate on the contributions most directly related to the development of Maxwell’s Equations. ![]() To name all involved would amount to writing a Who’s Who of 18th and 19th century physics. The sciences of electricity and magnetism and their fusion as electromagnetism evolved through a series of advances from many different scientists. When combined these equations also describe the transmission of radio waves and the propagation of light. These equations can explain how your hair stands on end when you remove your nylon sweater, how a compass needle always points north, how a power station turbine can generate electricity, and how a loudspeaker can convert an electric current into sound. Equation 4 describes how a magnetic field curls around a time-varying electric field or an electric current flowing in a conductor. Equation 3 describes how a time-varying magnetic field will cause an electric field to curl around it. The second pair, Equation 3 and Equation 4, describes how electric and magnetic fields are related. Equation 2 shows that magnetic field lines curl to form closed loops (Figure 4), with the implication that every north pole of a magnet is accompanied by a south pole. It shows that the electric field lines diverge from areas of positive charge and converge onto areas of negative charge (Figure 3). Equation 1 describes the electric force field surrounding a distribution of electric charge ρ. The first pair consists of Equation 1 and Equation 2. The equations can be considered in two pairs. The magnetic force fields are described by H (the magnetic field) and B = µ H (the magnetic flux density), the latter accounting for the magnetization of a material.įigure 4: Magnetic field lines around a bar magnet (left) and a current-carrying wire (right). The electric force fields are described by the quantities E (the electric field) and D = ε E (the electric displacement), the latter including how the electrical charges in a material become polarized in an electric field. The equations are shown in modern notation in Figure 2. In the modern context, Maxwell’s Equations refer to a set of four relations that describe the properties and interrelations of electric and magnetic fields. To set the context for the discovery and development of Maxwell’s Equations it is first important to understand what they are. The theory of electromagnetism was built on the discoveries and advances of many scientists and engineers, but the pivotal contribution was that of Maxwell, who during the second half of the 19th century made the huge conceptual leaps that would enable the great advances in electrical technology throughout the 20th century. Today, Maxwell’s Equations are the essential tool of electrical engineers, used to design all electrical and electronic equipment from cell phones to satellites, televisions to computers and power stations to washing machines. They are named after James Clerk Maxwell (Figure 1), the Scottish physicist whose pioneering work unified the theories of electricity, magnetism, and light. Maxwell’s Equations provide a complete description of electromagnetic phenomena and underpin all modern information and communication technologies. ![]() Figure 2: Maxwell’s Equations in modern vector form ( D = ε E B = µ H).
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