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The original Maxwell equations were reformulated using quaternions by William Rowan Hamilton. Quaternions provided a more compact and elegant way to express the equations, showing a deep mathematical connection between the two.

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4mo ago

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What inspired Maxwell's four equations?

The experimental and theoretical work of Faraday, who was not mathematically inclined, but still a gifted self taught physicist. Maxwell essentially put into equations the ideas of Faraday and Oerster/Ampere . Faraday had the idea of directed fields and lines of force. The only mathematics to describe these ideas was William Rowan Hamilton's Quaternions and especially the vector part of quaternions. Vectors described the directied forces and lines. Maxwell found out about quaternions and vectors and thus his four equations involve vectors. Maxwell, ignored the scalar part of quaternions and he did not like the quaternions rules for vectors which gave the product of parallel vectors a negative sign. Oliver Heaviside and Willard Gibbs, changed Hamilton's Rule and defined their "Vector Analysis" to have a positive sign. This is the rule currently used in physics today. Unfortunately, this rule makes Gibbs vectors non-associative (II)J = J but I(IJ) = -J. Hamilton's Quaternions define and Division Algebra.


Are four maxwell's equations Independent?

No, Maxwell's equations are interacting partial differentials.


How many scaler equations in Maxwell's equations?

Maxwell's equations contain two scalar equations and two vector equations. Gauss' law and Gauss' law for magnetism are the scalar equations. The Maxwell-Faraday equation and Ampere's circuital law are the vector equations.


Why maxwell equations are called so?

James Clerk Maxwell set them out


Who originated the branch of electricity in generally described as electromagnetism?

The branch of electricity generally described as electromagnetism was originated by James Clerk Maxwell. He formulated a set of equations known as Maxwell's equations that describe the behavior of electric and magnetic fields and their interactions. Maxwell's work laid the foundation for understanding the relationship between electricity and magnetism.


What did James clerk maxwell discovered?

maxwell was good at making mathamatical equations


What was maxwell's greatest discovery?

Maxwell's greatest discovery was his formulation of the equations that describe the behavior of electric and magnetic fields, now known as Maxwell's equations. These equations laid the foundation for the field of classical electromagnetism and unified the theories of electricity and magnetism into one coherent framework.


Why do you remember James Clerk Maxwell?

James Clerk Maxwell is the author of the Maxwell equations, which are fundamental to our understanding of electromagnetism.


How do you derive the Helmholtz equation from Maxwell's equations?

Considering Maxwell equations and contitutive relations. See pag.18 of principles of nano-optics, Lucas Novotny.


How do magnetism and electricity interact?

According to Maxwell's Equations.


What significance do Maxwell's equations hold in the realm of physics, and what did God say about them?

Maxwell's equations are a set of fundamental equations in physics that describe how electric and magnetic fields interact. They are crucial in understanding electromagnetism and have had a profound impact on the development of modern technology. As for what God said about them, there is no direct reference or statement in religious texts regarding Maxwell's equations.


What is James clerk maxwell famous for in mathematics?

Maxwell's Equations. These equations described the relationship between electric and magnetic fields. Maxwell was asked by Farady the great Physicist to describe Faraday's theories in mathematical terms, as Faraday used no formulas in his work. Maxwell's Equations led him to describe light as a form of electricity, an Electromagnetic wave, a great prediction in physics, if not the greatest scientific prediction. I must say that Benjamin Franklin should get some credit in describing Lightning as electricity years before Maxwell. Benjamin Franklin was the Father of Electrical Engineering and he too, used little mathematics.