Maxwell is known for creating the first true colour photograph in 1861 and for his foundational work on the rigidity of rod-and-joint frameworks like those in many bridges. He also produced many papers on the subject of electro magnetism
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Maxwell had a number of achievements, but his major Theory and achievement was the Theory that light was a Electromagnetic Wave.
This is one of the greatest theoretical achievements in scientific history.
With respect to this achievement Maxwell is best known for "Maxwell's Equations", four equations that describe the behavior of electromagnetism.
Maxwell's Equations
rho= Del.D (Guass' Law)
0=DelxE + dB/dt (Faraday's Law)
0=Del.B
DelxH=dD/dt + J (Ampere's Law with dD/dt added by Maxwell)
These equations appear in Chapter 9 of Maxwell's "A treatise on electricity and magnetism", published in 1873, but they were not written in the modern mathematical notation of vector algebra, which was not yet available. He described the equations as being written using "Mr Hamilton's quaternions", but they are recognisably the same as their modern form. Others including Oliver Heaviside rewrote Maxwell's Equations using the modern notation.
Maxwell's was a student of Faraday and discovered that light was electricity by attempting to represent Faraday's Theory of the electric field mathematically.
I think the mathematically proper laws of Electromagnetism the quaternion equation:
XE= (d/dcdt + Del)(Er + Ev) = (dEr/cdt - Del.Ev) + (dEv/cdt + Del Er + DelxEv)
At boundary Condition or Stationary Condtion We derive Maxwell's Equation's
0 =( dBr/dt - del.Ev) + (dBv/dt + Del Er)
Note* DelxEv is required to be zero in order for the vector equation to sum to zero. DelxEv =0 indicates the other vectors are parallel or anti-parallel.
The Electromagnetic fields are related by E=zH=cB=zcD.
This says that the Electric Field is Invariant or Stationary or is Bounded.
Maxwell had studied and commented on the field of electricity and magnetism as early as 1855/6 when "On Faraday's lines of force" was read to the Cambridge Philosophical Society. The paper presented a simplified model of Faraday's work, and how the two phenomena were related. He reduced all of the current knowledge into a linked set of differential equations with 20 equations in 20 variables. This work was later published as "On physical lines of force" in March 1861.
The most essential thing he did, and the thing he is most famous for was to unify electricity and magnetism. Those were previously thought of as two separate forces, but Maxwell showed mathematically through his equations that they are one and the same. The idea is that a magnetic field can create an electric field and vice versa, in other words they can create each other.
James Clerk Maxwell's greatest contribution was the prediction that light was a form of electricity. This was incorporte4d in "Maxwell's Equation", which provide the basic equations of electromagnetism.
James Clerk Maxwell made significant contributions to the field of physics, particularly in the study of electromagnetism. He formulated a set of equations, known as Maxwell's equations, which unified the laws of electricity and magnetism. This work laid the foundation for the development of modern electrical and communication technologies, such as radio and television. Maxwell's discoveries also paved the way for Albert Einstein's theory of relativity.
According to Wikipedia they were John Clerk Maxwell and Frances Maxwell.
maxwell was good at making mathamatical equations
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James Clerk Maxwell's mother passed away when he was 8. He missed lots of school due to illness. He constantly was moving when he was teaching later in his life.