Physics of light and optics by Justin Peatross; Michael Ware

By Justin Peatross; Michael Ware

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Gauss made important advances in number theory and differential geometry. He developed the law discussed here as one of Maxwell’s equations in 1835, but it was not published until 1867, after Gauss’ death. Ironically, Maxwell was already using Gauss’ law by that time. 12) The latter equation is known as the Biot-Savart law. The permeability µ0 dictates the strength of the magnetic field, given the current distribution. As with Coulomb’s law, we can apply mathematics to the Biot-Savart law to obtain another of Maxwell’s equations.

We therefore will write ρ free = 0. One might be tempted in this case to set the overall charge density ρ to zero, but this would be wrong. The polarization of a neutral material, described by P, can vary spatially, leading to local concentrations of positive or negative charges. We let ρ p denote the charge density created by variations in the polarization P(r). 32) is a surface integral, which after integrating gives units of charge. Physically, it is the sum of the charges touching the inside of surface S (multiplied by a minus since by convention dipole vectors point from the negatively charged end of a molecule to the positively charged end).

He founded the Cavendish laboratory at Cambridge in 1874, which has produced 28 Nobel prizes to date. Maxwell, one of Einstein’s heros, died of stomach cancer in his forties. 19). 4). This revised Ampere’s law includes the additional term 0 ∂E/∂t , which is known as the displacement current (density). 10 It indicates that a changing electric field behaves like a current in the sense that it produces magnetic fields. 4) is apparent. No doubt this played a part in motivating Maxwell’s work. In summary, in the previous section we saw that the basic physics in Ampere’s law is present in the Biot-Savart law.

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