Maxwell's Electromagnetism

When Maxwell began developing his theory of electromagnetism, many of its separate aspects had already been understood by Michael Faraday and others. In attempting to unite the different laws, Maxwell uncovered a mathematical inconsistency between the different equations, which he resolved by adding a new mathematical term (now called Maxwell’s term) to his equations. This term was difficult to measure in the laboratory, but he did notice that it implied the existence of waves made up of electric and magnetic fields, moving at a speed that his equations predicted to be close to what was then estimated as the speed of light. This inspired Maxwell to postulate that light is nothing but an electromagnetic wave! ¹ This was yet another demonstration of the power of mathematical logic to predict new physical phenomena: Maxwell’s correction arose from mathematical rather than physical considerations. His discovery of a simple mathematical inconsistency led him to conclude that light is made up of electric and magnetic disturbances moving through space–a triumph of human thought! This is one among countless examples showing that mathematical principles can be sufficient to motivate new physical laws.