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Displacement Current and Maxwell’s Equations

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Part of the Undergraduate Lecture Notes in Physics book series (ULNP)

Abstract

In a steady state, Ampere’s law, Eq. (9.14), holds for a closed line, C, with different surfaces on it, S1 and S2, as shown in Fig. 11.1a, b. If the magnetic field \(\boldsymbol{H}\) is integrated on C in opposite directions as drawn in Fig. 11.1a, b, the sum of the two integrations is naturally zero. At the same time, the sum of the surface integrals of the current density \(\boldsymbol{i}\) on S1 and S2 is also zero. This sum becomes the surface integral on closed surface S12 composed of S1 and S2 (see Fig. 11.1c). Thus, we have

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Matsushita, T. (2014). Displacement Current and Maxwell’s Equations. In: Electricity and Magnetism. Undergraduate Lecture Notes in Physics. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54526-2_11

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