In the above, ℰ is the electric field, ℬ is the magnetic field, ρ is the charge density, and j is the current density. In natural Lorentz-Heaviside units, they take the following form. In 1861, James Clerk Maxwell corrected and combined four disparate equations that had been known in one form or another in order to create a comprehensive theory of electromagnetism. So what exactly are Maxwell’s equations? They are a set of four partial differential equations that describe how electric and magnetic fields respond to charges, currents, and each other. And with Mathematica 9’s new vector analysis functionality, exploring them has never been easier. ![]() There are many reasons to love Maxwell’s equations. The quantum version of the equations, quantum electrodynamics (QED), remains our most successful physical theory, with predictions verified to 12 decimal places. On a more universal level, the hints in Maxwell’s equations led Einstein to write Zur Elektrodynamik bewegter Körper (“On the Electrodynamics of Moving Bodies”), more commonly known as Einstein’s first paper on the theory of relativity. ![]() As a freshman in college, while pondering whether to major in physics, computer science, or music, it was the beauty of these equations and the physical predictions that can be elegantly extracted from them that made me decide in favor of physics.
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