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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.01518 |
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| _version_ | 1866912516738646016 |
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| author | Luna, Benjamin K. Daw, Murray S. |
| author_facet | Luna, Benjamin K. Daw, Murray S. |
| contents | Set up a charged rectangular-plate capacitor in a uniform $\mathbf{B}$-field. Quasi-statically turn off the $\mathbf{B}$-field - what happens? We show that this seemingly simple induction problem (which appears in a famous undergraduate electrodynamics textbook) highlights the causal structure of electrodynamics. It may be (as it is in this problem) that different source configurations can produce the same uniform $\mathbf{B}$-field over some finite region, but very different dynamics when the source is turned off. We see also that the vector potential gives more information about the source of the $\mathbf{B}$-field, and is a very useful (and under-appreciated) way to understand induction and other key aspects of electrodynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01518 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Not All Uniform B-Fields Are The Same! Luna, Benjamin K. Daw, Murray S. Classical Physics Set up a charged rectangular-plate capacitor in a uniform $\mathbf{B}$-field. Quasi-statically turn off the $\mathbf{B}$-field - what happens? We show that this seemingly simple induction problem (which appears in a famous undergraduate electrodynamics textbook) highlights the causal structure of electrodynamics. It may be (as it is in this problem) that different source configurations can produce the same uniform $\mathbf{B}$-field over some finite region, but very different dynamics when the source is turned off. We see also that the vector potential gives more information about the source of the $\mathbf{B}$-field, and is a very useful (and under-appreciated) way to understand induction and other key aspects of electrodynamics. |
| title | Not All Uniform B-Fields Are The Same! |
| topic | Classical Physics |
| url | https://arxiv.org/abs/2508.01518 |