Maxwell's Equations |
Maxwell Legacy Concepts |
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In a nutshell |
Nowadays we talk of a 'magnetic field' or an 'electric field' as if these ideas were obvious. It was Maxwell who gave substance to these terms. Before his time they had been just metaphors of Michael Faraday to represent the influence of sources of magnetism and electricity. Maxwell showed that these fields could be expressed mathematically by equations that describe their behaviour and interactions. He derived his equations from the known laws of electricity and magnetism, with some additional crucial insight of his own. Maxwell's equations have survived the revolutionary changes of 20th century physics and they underpin a huge range of natural phenomena. In particular they predict the possible existence of electromagnetic waves and how they behave, including light and radio waves. |
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Technical detail | Maxwell's equations on a plaque beside his statue in George Street, Edinburgh Maxwell's equations date from the early 1860s but the elegant four lines that are usually quoted today use the vector notation introduced by Oliver Heaviside in the 1880s. Fields diverge when they have point sources. The first equation on the right (∇. With these equations, Maxwell showed that in free space electric and magnetic fields obey a wave equation whose solution has the properties of light and radiant heat. One property of the solution is that in free space both the electric and magnetic fields are at right angles to the direction of propagation. This fitted exactly with the known polarisation properties of light. What clinched the association with light and heat for Maxwell was that the speed of propagation of electromagnetic waves was determined by constants known from purely electromagnetic experiments. They predicted a value for the speed of electromagnetic waves that within experimental error matched the measured speed of light. His prediction kick started refined experiments to measure the speed of light accurately (notably by Leon Foucault) and he himself undertook a very careful electromagnetic experiment to measure the electromagnetic constants more accurately. The net result of this experimental activity over several years confirmed Maxwell's prediction of electromagnetic waves travelling at the speed of light. When materials are involved, Maxwell's equations written so succinctly need to be unpacked. The relationship between Fields fill all space and a given field defines an influence at any point in space. The electric field is a vector quantity defining the magnitude and direction of the force on a unit charge placed at the point. The magnetic field defines the torque on a miniscule magnet, which is why iron filings show up magnetic field lines and compasses work. Maxwell showed how to formulate a field theory mathematically and hence quantitatively. 20th century physics has taken Maxwell's concepts and seen them as the way forward in describing the fundamental processes in nature. Quantum Field Theory is one result, General Relativity another. Fields are the modern reality. Maxwell, well before anyone today was born, showed how field theories could be constructed.
JSR 2016 |
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