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Maxwell - Maxwell’s Equations Maxwell’s Equations...

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Unformatted text preview: Maxwell’s Equations Maxwell’s Equations aren’t really Maxwell’s—with the possible exception of the last one. They are Gauss’s, Faraday’s, and Ampère’s, and you have mostly already been introduced to them: Gauss’s law says that the electric field through an enclosing surface is proportional to the charge inside: E = Q in /A ε ₀ . Gauss also discovered that magnetic flux lines do not have starting or ending points, but so far we have treated that as a concept instead of an equation. Faraday’s law, meantime, was used to predict the induced voltage from a changing magnetic flux: V = -N ∆ Φ / ∆ t . Finally, Ampère’s law was employed to predict the magnetic field encircling a linear current-carrier: B = µ ₀ I/2 π r . All of these equations can be stated in a more general form using calculus. Imagine that we are no longer limited to spheres, cylinders, and planes in applying Gauss’s law, but can instead add up (integrate) all the electric field in every direction passing through a...
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