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 = μ0 ( 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 = ± ( μ0 i d 2 πR 2 ) r r ≤ R μ0 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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