Maxwell’s Equations in a Nutshell

Abstract

Light has fascinated us for ages. And deservedly so. Everything we know about the earth and the universe is because of light. Light from the sun sustains life on earth. Learning to measure and understand the contents of light has enabled us to understand the origins of the universe in the big bang, and talk about its future. And one cannot forget the sheer visual pleasure of a beautiful sunset, a coral reef, or an iridescent flower in full blossom. Indeed, the beauty of light and color is a rare thing that scientists and artists agree to share and appreciate. Our fascination with light has led to three of the greatest revolutions in 19 th and 20 th century physics. Sunlight used to be considered a 'gift of the Gods' and the purest indi-visible substance, till Newton observed that passing it through a prism split it into mul-tiple colors. Passing each of the colors through another prism could not split it further. Newton surmised that light was composed of particles, but in the early 19 th century, Young proved that light was a wave because it exhibited interference and di↵raction. Michael Faraday had a strong hunch that light was composed of a mixture of electric and magnetic fields, but could not back it up mathematically. The race for understanding the fabric of light reached a milestone when Maxwell gave Faraday's hunch a rigorous math-ematical grounding. Maxwell's theory combined in one stroke electricity, magnetism, and light into an eternal braid 1 . The Maxwell equations predict the existence of light 1 J. R. Pierce famously wrote " To anyone who is motivated by anything beyond the most narrowly practical, it is worthwhile to understand Maxwell's equations simply for the good of his soul. " 132