Saturday, December 24, 2022

Why Is Electrodynamics Constrained By Heaviside's Condensed Version Of Maxwell's Equations?

wikipedia |  Oliver Heaviside FRS[1] (/ˈhɛvisd/; 18 May 1850 – 3 February 1925) was an English self-taught mathematician and physicist who invented a new technique for solving differential equations (equivalent to the Laplace transform), independently developed vector calculus, and rewrote Maxwell's equations in the form commonly used today. He significantly shaped the way Maxwell's equations are understood and applied in the decades following Maxwell's death. His formulation of the telegrapher's equations became commercially important during his own lifetime, after their significance went unremarked for a long while, as few others were versed at the time in his novel methodology.[2] Although at odds with the scientific establishment for most of his life, Heaviside changed the face of telecommunications, mathematics, and science.[2]

Heaviside's uncle by marriage was Sir Charles Wheatstone (1802–1875), an internationally celebrated expert in telegraphy and electromagnetism, and the original co-inventor of the first commercially successful telegraph in the mid-1830s. Wheatstone took a strong interest in his nephew's education[5] and in 1867 sent him north to work with his older brother Arthur Wheatstone, who was managing one of Charles' telegraph companies in Newcastle-upon-Tyne.[4]: 53 

Two years later he took a job as a telegraph operator with the Danish Great Northern Telegraph Company laying a cable from Newcastle to Denmark using British contractors. He soon became an electrician. Heaviside continued to study while working, and by the age of 22 he published an article in the prestigious Philosophical Magazine on 'The Best Arrangement of Wheatstone's Bridge for measuring a Given Resistance with a Given Galvanometer and Battery'[6] which received positive comments from physicists who had unsuccessfully tried to solve this algebraic problem, including Sir William Thomson, to whom he gave a copy of the paper, and James Clerk Maxwell. When he published an article on the duplex method of using a telegraph cable,[7] he poked fun at R. S. Culley, the engineer in chief of the Post Office telegraph system, who had been dismissing duplex as impractical. Later in 1873 his application to join the Society of Telegraph Engineers was turned down with the comment that "they didn't want telegraph clerks". This riled Heaviside, who asked Thomson to sponsor him, and along with support of the society's president he was admitted "despite the P.O. snobs".[4]: 60 

In 1873 Heaviside had encountered Maxwell's newly published, and later famous, two-volume Treatise on Electricity and Magnetism. In his old age Heaviside recalled:

I remember my first look at the great treatise of Maxwell's when I was a young man... I saw that it was great, greater and greatest, with prodigious possibilities in its power... I was determined to master the book and set to work. I was very ignorant. I had no knowledge of mathematical analysis (having learned only school algebra and trigonometry which I had largely forgotten) and thus my work was laid out for me. It took me several years before I could understand as much as I possibly could. Then I set Maxwell aside and followed my own course. And I progressed much more quickly... It will be understood that I preach the gospel according to my interpretation of Maxwell.[8]

Undertaking research from home, he helped develop transmission line theory (also known as the "telegrapher's equations"). Heaviside showed mathematically that uniformly distributed inductance in a telegraph line would diminish both attenuation and distortion, and that, if the inductance were great enough and the insulation resistance not too high, the circuit would be distortionless in that currents of all frequencies would have equal speeds of propagation.[9] Heaviside's equations helped further the implementation of the telegraph.

 

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