The Laws of Electricity and Magnetism

Electrostatics gives a description of the forces between charges distributed in a known manner in space. This description is greatly facilitated by introducing the electrical field E which is the force per unit charge q. Both the force F and the field E are vectors whereas the charge is a scalar quantity. The relationship between F and E is 

Gauss law relaLes Lhe field due Lo a eolleeLion of charges to the magnitude of charges. Thus, 

5 is a surface which surrounds the charges, for example, a sphere. is a vector perpendicular to the surface. The integration is carried out over the surface area a. Both Coulomb s law and Gauss law have been written here for charges in a vacuum. This law may be used to estimate the field due to a uniform distribution of charges. A well-known example is the field due to charge on the surfaces of a parallel-plate capacitor. For this system, the field is 

The electrical potential is defined as the work done to move a test charge from one point in a field to another. Suppose the potential difference is estimated between a point located a distance ri from a point charge q to a point located a distance r2- The difference in potential is 

The minus sign expresses the fact that work is done and the energy of the system increases when the positive test charge moves against the field. The general expression for the potential due to a point charge q is 

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This result was experimentally discovered in the nineteenth century, but it could not be explained by Maxwells theory of electromagnetism. (James Clerk Maxwell was a Scottish physicist whose formulation of the laws of electricity and magnetism were... 

One problem remained, that of explaining why the orbiting electrons didn t lose energy and fall into the nucleus. Bohr solved the problem by making the assumption that the laws of electricity and magnetism that said this should happen simply didn t apply to events on the subatomic level. This was the most audacious part of his theory. Never before had any physicist been willing to assume that the known laws of physics were inoperable under certain circumstances. 

Lewis assumed that the laws of electricity and magnetism are... 

To end this chapter it is useful to generalize all the aspects discussed they compose a system of equations of classical Maxwellian electrodynamics from which all the laws of electricity and magnetism can be derived, including electromagnetic radiation. Nearly all the equations are already known to the readers, so we can concentrate mainly on the physical conclusions. 

The latter half of the nineteenth century was a time of intellectual triumph in the physical sciences. Most of the material contained in the first year of modem college physics courses was completely understood by then. Newton s laws had been rephrased in different mathematical forms which simplified even complicated many-body problems such as planetary motion. In addition, the description of electric and magnetic fields by Maxwell s equations was an essentially complete success—so much so that these equations and their consequences are the central focus of some graduate physics courses even today. 

The characteristic spectrum of blackbodies was determined experimentally in the nineteenth century. But it could not be explained by the physics of Newton and Maxwell. (The great English scientist Isaac Newton formulated the laws of motion and gravity in 1687 James Clerk Maxwell, a Scottish physicist, published his laws of electricity and magnetism in 1871.)... 

Scottish physicist James Clerk Maxwell, who developed the theory of electricity and magnetism in the late 1800s, proposed that Faraday s laws required that one molecule of positive and negative electricity is involved in electrolysis. Irish physicist George Johnstone Stoney believed in this molecule of electricity and set out to measure the definite quantity of electricity, called el. He suggested that if this unit of electricity was adopted, it would represent a very important step in our study of molecular phenomena. In 1891 Stoney referred to these charges as electrons. The controversy of the day then revolved around whether these electrons were waves or particles. 

The battery invented by Alessandro Volta (1745-1827) in 1799 consisted of layers of Zn and Ag separated by cardboard soaked in brine. This voltaic pile on display at the Royal Institution in London was given by Volta to Humphry Davy and Michael Faraday when they visited Italy in 1814. Using electrolysis, Davy was the first to isolate Na, K, Mg, Ca, Sr, and Ba. Faraday used piles to discover laws of electricity and magnetism. 

FIGURE 4.3 James Clerk Maxwell (1831-1879), Scottish mathematician. Maxwell made many important contributions before his untimely death just before his 48th birthday. Among them is the Maxwell theory of electromagnetism, which even today forms the basis of electrical and magnetic behavior. He also contributed to the kinetic theory of gases and the development of the second law of thermodynamics. He was one of the few people to understand Gibbs s work. 

Faraday is better known in chemistry for his laws of electrolysis and in physics for proposing the relationship between electric and magnetic fields and for demonstrating the principle of electromagnetic induction. 

We will first consider the laws of Coulomb, Biot-Savart and Faraday, emphasizing their experimental origin and the areas in which they can be applied. The relationship between these laws and Maxwell s equations will then be described to further explore their physical meaning and especially the precise sources of electric and magnetic fields. 

Charles Augustin de Coulomb (1736-1806), French military engineer and one of the founders of quantitative physics. In 1777, he constructed a torsion bal-ance for measuring very weak forces, with which he was able to demonstrate the inverse square (of the distarx e) law for electric and magnetic forces. 

Maxwell s equations, which were first presented in 1864 and published in 1865 [40], completely describe the classical behavior of electric and magnetic fields and — supported by the Lorentz force law — their interaction with charged particles and currents. In Gaussian units their differential form is given by... 

Charged particles exert forces that conventionally are described in terms of electric and magnetic fields. Consider two particles with charges qi and located at positions r and r2 in a vacuum. According to Coulomb s law, the electrostatic force acting on particle 1 is... 

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