![]() Understanding electricity and magnetism allows us to understand behavior at all physical scales, helping to explain physical phenomena ranging from why protons and electrons are attracted to one another in atomic nuclei to how light can be generated by the motion of charged particles. Ultimately, the electric and magnetic fields represent the way in which charged particles interact with one another, just as celestial bodies gravitationally attract.Īs we shall see throughout the remainder of this post, charged objects are both affected by the presence of these fields and capable of creating new ones, thereby tethering the seemingly intangible fields to physical objects which fall into our standard, observational reality. ![]() Electric charge $Q_e$ and magnetic charge $Q_m$ will feel forces from the various fields, thereby allowing us to measure them. Mathematically, we represent them as vector fields, basically arrows (each with their own magnitude and direction) at each point in space. The electric and magnetic fields, which are measures of the strength of electric and magnetic forces, permeate the space all around us. IntroductionĮlectricity and Magnetism are among the most fundamental forces of nature. More than anything, the purpose is to imbue the reader with some of the physical intuition behind electromagnetism. Example: Calculating the wavelength of a light wave What is the wavelength of this wave We can start with our equation that relates frequency, wavelength. Here, I aim to delve into the fundamentals of electromagnetism, with the goal of making this post accessable to those who may not have a particularly strong mathematical background while including enough analysis so that it may be useful and interesting to those who do. I was quite proud of my response (and it earned the highest grade in the class), so I have included it here in an effort to convey my passion for these elegant, and profound, equations. Our responses were not supposed to be steeped in derivations or overly sophisticated equations, but were instead supposed to build intuition. S x y z dr dx dy dz ds ds ds ds ds length element along curve let’s consider some very simple examples. A reminder on differential line elements. In words, the change in the optical path along the path is given by the gradient in the index of refraction. Jim Fujimoto, who pioneered optical coherence tomography.ĭescribe the Physics behind Maxwell's Equations.ĭeceptively simple, the prompt was designed to encourage me and my peers to think more about the physical implications of the well-known Maxwell’s Equations, which detail the behavior of electromagnetism, one of the fundamental forces of nature. of the light, this differential equation governs the path taken. The original motivation for this post was the first homework prompt I encountered in graduate school at MIT, while I was taking a course on linear optics:
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