CourseNotes.54 - The reason that the four equations are...

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The reason that the four equations are associated with Maxwell even though he only added one small term is because after adding this term Maxwell showed that light is an electromagnetic wave. This tied together the fields of optics and electromagnetism, which until then had been completely separate. Maxwell’s term is often called the displacement current because we can rewrite Ampere’s law in a form which appears to have two currents on the rhs. I ~ B · d ~ S = μ 0 ( i d + i enc ) where i d = ± 0 d Φ E dt Thinking of this term as a sort of current is also good analogy for thinking about the magnetic field between the capacitor plates. If we apply Ampere’s law to a circular parallel plate capacitor of radius R , then we find that the field inside of the capacitor looks like B = ± ( μ 0 i d 2 πR 2 ) r r R μ 0 i d 2 πr r > R So, we see that the field outside of the capacitor looks the same as it would outside a wire carrying a current i d . 13.3 Magnetism at the Atomic Level
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