#ScienceSunday In honor of our next generation of lawyers who are taking the Bar Exams this month, this weeks #ScienceSunday will feature #ScientificLaws A scientific law can often be reduced to a mathematical statement, such as E = mc²; its a specific statement based on empirical data, and its truth is generally confined to a certain set of conditions. For example, in the case of E = mc², c refers to the speed of light in a vacuum. #MaxwellEquations Maxwells Equations are a set of partial differential equations that form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields, in turn, underlie modern electrical and communications technologies. Maxwells Equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents. They are named after the Scottish physicist and mathematician James Clerk Maxwell, who published an early form of those equations between 1861 and 1862. 1. Gausss Law describes the relationship between a static electric field and the electric charges that cause it: The static electric field points away from positive charges and towards negative charges. In the field line description, electric field lines begin only at positive electric charges and end only at negative electric charges. Counting the number of field lines passing though a closed surface, therefore, yields the total charge (including bound charge due to polarization of material) enclosed by that surface divided by dielectricity of free space (the vacuum permittivity). More technically, it relates the electric flux through any hypothetical closed Gaussian surface to the enclosed electric charge. 2. Gausss Law for Magnetism states that there are no magnetic charges (also called magnetic monopoles), analogous to electric charges. Instead, the magnetic field due to materials is generated by a configuration called a dipole. Magnetic dipoles are best represented as loops of current but resemble positive and negative magnetic charges, inseparably bound together, having no net magnetic charge. 3. Faradays Law describes how a time varying magnetic field creates (induces) an electric field. This dynamically induced electric field has closed field lines just as the magnetic field, if not superposed by a static (charge induced) electric field. This aspect of electromagnetic induction is the operating principle behind many electric generators: for example, a rotating bar magnet creates a changing magnetic field, which in turn generates an electric field in a nearby wire. 4. Ampères Law with Maxwells addition states that magnetic fields can be generated in two ways: by electrical current (this was the original Ampères Law) and by changing electric fields (this was Maxwells addition). Maxwells addition to Ampères law is particularly important: it shows that not only does a changing magnetic field induce an electric field, but also a changing electric field induces a magnetic field. Therefore, these equations allow self-sustaining electromagnetic waves to travel through empty space.
Posted on: Sun, 19 Oct 2014 05:37:17 +0000
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