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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2412.13221 |
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| _version_ | 1866918334870585344 |
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| author | Biswas, Shyamal |
| author_facet | Biswas, Shyamal |
| contents | We have re-examined the integral form of Gauss' law for arbitrarily moving charges inside and outside an arbitrarily expanding (or contracting) and deforming Gaussian surface. We have explicitly calculated the time-dependent Gauss' flux integral for such a generic non-static case with the Maxwell equations under consideration. We have obtained an evolution equation $\frac{\text{d}}{\text{d}\text{t}}\oint_{s(t)}\vec{E}\cdot\text{d}\vec{s}(t)=\frac{I^{(s)}_{\text{in}}(t)}{ε_0}$ for the time-dependence of the flux-integral. We have pedagogically demonstrated that while the flux integral is dependent on the expansion/contraction of the surface, it is independent of its deformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13221 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Revisiting the integral form of Gauss' law for a generic case of electrodynamics with arbitrarily moving Gaussian surface Biswas, Shyamal Classical Physics We have re-examined the integral form of Gauss' law for arbitrarily moving charges inside and outside an arbitrarily expanding (or contracting) and deforming Gaussian surface. We have explicitly calculated the time-dependent Gauss' flux integral for such a generic non-static case with the Maxwell equations under consideration. We have obtained an evolution equation $\frac{\text{d}}{\text{d}\text{t}}\oint_{s(t)}\vec{E}\cdot\text{d}\vec{s}(t)=\frac{I^{(s)}_{\text{in}}(t)}{ε_0}$ for the time-dependence of the flux-integral. We have pedagogically demonstrated that while the flux integral is dependent on the expansion/contraction of the surface, it is independent of its deformation. |
| title | Revisiting the integral form of Gauss' law for a generic case of electrodynamics with arbitrarily moving Gaussian surface |
| topic | Classical Physics |
| url | https://arxiv.org/abs/2412.13221 |