Maxwell’s Equations: Electromagnetic Waves Predicted and Observed Quiz

PDF page 1155: The Scotsman James Clerk Maxwell (1831–1879) is regarded as the greatest theoretical physicist of the 19th century. (See Figure 24.3.) Although he died young, Maxwell not only formulated a complete electromagnetic theory, represented by Maxwell’s equations, he also developed the kinetic theory of gases and made significant contributions to the understanding of color vision and the nature of Saturn’s rings.

PDF page 1155: The Scotsman James Clerk Maxwell (1831–1879) is regarded as the greatest theoretical physicist of the 19th century. (See Figure 24.3.) Although he died young, Maxwell not only formulated a complete electromagnetic theory, represented by Maxwell’s equations, he also developed the kinetic theory of gases and made significant contributions to the understanding of color vision and the nature of Saturn’s rings.

PDF page 1156: magnetism and correctly predicted that visible light is caused by electromagnetic waves. (credit: G. J. Stodart) Maxwell brought together all the work that had been done by brilliant physicists such as Oersted, Coulomb, Gauss, and Faraday, and added his own insights to develop the overarching theory of electromagnetism. Maxwell’s equations are paraphrased here in words because their mathematical statement is beyond the level of this text. However, the equations illustrate how apparently simple mathematical statements can elegantly unite and express a multitude of concepts—why mathematics is the language of science.

PDF page 1156: defined as the force per unit charge on a test charge, and the strength of the force is related to the electric constant , also known as the permittivity of free space. From Maxwell’s first equation we obtain a special form of Coulomb’s law known as Gauss’s law for electricity.

PDF page 1156: exist. The strength of the magnetic force is related to the magnetic constant , also known as the permeability of free space. This second of Maxwell’s equations is known as Gauss’s law for magnetism.

PDF page 1156: exist. The strength of the magnetic force is related to the magnetic constant , also known as the permeability of free space. This second of Maxwell’s equations is known as Gauss’s law for magnetism.

PDF page 1156: 3. A changing magnetic field induces an electromotive force (emf) and, hence, an electric field. The direction

PDF page 1156: of the emf opposes the change. This third of Maxwell’s equations is Faraday’s law of induction, and includes Lenz’s law.

PDF page 1156: equations encompasses Ampere’s law and adds another source of magnetism—changing electric fields.

PDF page 1156: Maxwell’s equations encompass the major laws of electricity and magnetism. What is not so apparent is the symmetry that Maxwell introduced in his mathematical framework. Especially important is his addition of the hypothesis that changing electric fields create magnetic fields. This is exactly analogous (and symmetric) to Faraday’s law of induction and had been suspected for some time, but fits beautifully into Maxwell’s equations. Symmetry is apparent in nature in a wide range of situations. In contemporary research, symmetry plays a major

PDF page 1156: Maxwell’s complete and symmetric theory showed that electric and magnetic forces are not separate, but different manifestations of the same thing—the electromagnetic force. This classical unification of forces is one motivation for current attempts to unify the four basic forces in nature—the gravitational, electrical, strong, and weak nuclear forces.

PDF page 1157: Maxwell’s hypothesis. Maxwell realized, however, that oscillating charges, like those in AC circuits, produce changing electric fields. He predicted that these changing fields would propagate from the source like waves generated on a lake by a jumping fish. The waves predicted by Maxwell would consist of oscillating electric and magnetic fields—defined to be an electromagnetic wave (EM wave). Electromagnetic waves would be capable of exerting forces on charges great distances from their source, and they might thus be detectable. Maxwell calculated that electromagnetic waves would propagate at a speed given by the equation