Abstract
Amperes circuital law is a very important formula in classical electromagnetics. However, the corresponding detailed theoretical derivation is rarely seen in relevant textbooks. In this paper, based on the magnetic field produced by a moving charge, we taken the divergence theorem and rotation of the magnetic field, respectively, and given a series of mathematical transformations. At last, we derived Ampere's circuital law of the magnetic field, which is very helpful to understand the physical source of the law.
Highlights
Ampere circuital law is a very important formula in classical electromagnetics, but it is almost directly given in many textbooks
For the magnetic field produced by the current carrying wire infinitely length, the theoretical derivation of Ampere's circuital law were reported. papers [1,2,3,4] show that the law had been derived by quantum mechanics, geometry and pure mathematics, respectively
Few papers have been reported that the theoretical derivation of Ampere's circuital law of magnetic field produced by a single moving charge or by the current carrying wire with finite length was been obtained
Summary
Ampere circuital law is a very important formula in classical electromagnetics, but it is almost directly given in many textbooks. Using the space solid angle to calculate the circuital integral of the magnetic field produced by the current carrying wire, we can directly derive Ampere circuital law. For the magnetic field produced by the current carrying wire infinitely length, the theoretical derivation of Ampere's circuital law were reported. Papers [1,2,3,4] show that the law had been derived by quantum mechanics, geometry and pure mathematics, respectively. Few papers have been reported that the theoretical derivation of Ampere's circuital law of magnetic field produced by a single moving charge or by the current carrying wire with finite length was been obtained. In this paper, based on the theoretical expression of the magnetic field generated by the moving charge, we taken the divergence and rotation of the magnetic field, respectively, and derived Ampere's law of the magnetic field, which is of much help to understand Ampere's law
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