![]() ![]() 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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