Файл:Eddy currents - explanation of drag force.svg

Описание

}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66e689b14d7dc8bc9592c4acfdaadbd6fc4ddf1f" style="vertical-align: -0.671ex; width:2.279ex; height:2.009ex;"/> shows an electron in the metal under the magnet right after it has undergone a collision, and [math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt msub\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt e\lt /mi\gt \lt /mrow\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mtext\gt 2\lt /mtext\gt \lt /mrow\gt \lt /msub\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle \mathbf {e} _{\text{2}}}\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle \mathbf {e} _{\text{2}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65b0a74a3ca2ad6eca0a97ad3ef5b62bf3681648" style="vertical-align: -0.671ex; width:2.279ex; height:2.009ex;"/> shows the same electron after it has been accelerated by the magnetic field. On average at [math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt msub\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt e\lt /mi\gt \lt /mrow\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mtext\gt 1\lt /mtext\gt \lt /mrow\gt \lt /msub\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle \mathbf {e} _{\text{1}}}\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle \mathbf {e} _{\text{1}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66e689b14d7dc8bc9592c4acfdaadbd6fc4ddf1f" style="vertical-align: -0.671ex; width:2.279ex; height:2.009ex;"/> the electron has the same velocity as the sheet [math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt v\lt /mi\gt \lt /mrow\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle \mathbf {v} }\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle \mathbf {v} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35c1866e359fbfd2e0f606c725ba5cc37a5195d6" style="vertical-align: -0.338ex; width:1.411ex; height:1.676ex;"/> (black arrow). in the [math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt mo\gt +\lt /mo\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt x\lt /mi\gt \lt /mrow\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle +\mathbf {x} }\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle +\mathbf {x} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/54c722029f50f473e7b166a1cf2d689f4960d182" style="vertical-align: -0.505ex; width:3.219ex; height:2.176ex;"/> direction. The magnetic field ([math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt B\lt /mi\gt \lt /mrow\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle \mathbf {B} }\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle \mathbf {B} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cafb0ef39b0f5ffa23c170aa7f7b4e718327c4d1" style="vertical-align: -0.338ex; width:1.901ex; height:2.176ex;"/>, green arrow) of the magnet's North pole N is directed down in the [math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt mo\gt −\lt !-- − --\gt \lt /mo\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt y\lt /mi\gt \lt /mrow\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle -\mathbf {y} }\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle -\mathbf {y} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29502381c2d9b0ffcfc7cca4a0db68f77bafaf6a" style="vertical-align: -0.671ex; width:3.219ex; height:2.343ex;"/> direction. The magnetic field exerts a Lorentz force on the electron (pink arrow) of [math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt msub\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt F\lt /mi\gt \lt /mrow\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mtext\gt 1\lt /mtext\gt \lt /mrow\gt \lt /msub\gt \lt mo\gt =\lt /mo\gt \lt mo\gt −\lt !-- − --\gt \lt /mo\gt \lt mi\gt e\lt /mi\gt \lt mo stretchy="false"\gt (\lt /mo\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt v\lt /mi\gt \lt /mrow\gt \lt mo\gt ×\lt !-- × --\gt \lt /mo\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt B\lt /mi\gt \lt /mrow\gt \lt mo stretchy="false"\gt )\lt /mo\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle \mathbf {F} _{\text{1}}=-e(\mathbf {v} \times \mathbf {B} )}\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle \mathbf {F} _{\text{1}}=-e(\mathbf {v} \times \mathbf {B} )}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b2a3963737a376e4db2e392e6766763886e3cb47" style="vertical-align: -0.838ex; width:16.689ex; height:2.843ex;"/>, where e is the electron's charge. Since the electron has a negative charge, from the right hand rule this is directed in the [math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt mo\gt +\lt /mo\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt y\lt /mi\gt \lt /mrow\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle +\mathbf {y} }\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle +\mathbf {y} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41216c18cd1496a09a8fe3b09917f5e55b2e153f" style="vertical-align: -0.671ex; width:3.219ex; height:2.343ex;"/> direction. At [math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt msub\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt e\lt /mi\gt \lt /mrow\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mtext\gt 2\lt /mtext\gt \lt /mrow\gt \lt /msub\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle \mathbf {e} _{\text{2}}}\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle \mathbf {e} _{\text{2}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65b0a74a3ca2ad6eca0a97ad3ef5b62bf3681648" style="vertical-align: -0.671ex; width:2.279ex; height:2.009ex;"/> this force gives the electron a component of velocity in the sideways direction ([math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt msub\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt v\lt /mi\gt \lt /mrow\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mtext\gt 2\lt /mtext\gt \lt /mrow\gt \lt /msub\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle \mathbf {v} _{\text{2}}}\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle \mathbf {v} _{\text{2}}}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb310cc9f48a386eb16f8c6cf0db7d928e7f2615" style="vertical-align: -0.671ex; width:2.465ex; height:2.009ex;"/>. black arrow) The magnetic field acting on this sideways velocity, then exerts a Lorentz force on the particle of [math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt msub\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt F\lt /mi\gt \lt /mrow\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mtext\gt 2\lt /mtext\gt \lt /mrow\gt \lt /msub\gt \lt mo\gt =\lt /mo\gt \lt mo\gt −\lt !-- − --\gt \lt /mo\gt \lt mi\gt e\lt /mi\gt \lt mo stretchy="false"\gt (\lt /mo\gt \lt msub\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt v\lt /mi\gt \lt /mrow\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mtext\gt 2\lt /mtext\gt \lt /mrow\gt \lt /msub\gt \lt mo\gt ×\lt !-- × --\gt \lt /mo\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt B\lt /mi\gt \lt /mrow\gt \lt mo stretchy="false"\gt )\lt /mo\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle \mathbf {F} _{\text{2}}=-e(\mathbf {v} _{\text{2}}\times \mathbf {B} )}\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle \mathbf {F} _{\text{2}}=-e(\mathbf {v} _{\text{2}}\times \mathbf {B} )}" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ea408b4fbfeb67de61c72659299a11331f446144" style="vertical-align: -0.838ex; width:17.743ex; height:2.843ex;"/>. From the right hand rule, this is directed in the [math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt mo\gt −\lt !-- − --\gt \lt /mo\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt x\lt /mi\gt \lt /mrow\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle -\mathbf {x} }\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle -\mathbf {x} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0a01370ff50ffc54518e7c4c1199279b0370f68" style="vertical-align: -0.505ex; width:3.219ex; height:2.176ex;"/>, opposite to the velocity [math]\displaystyle{ \lt semantics\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mstyle displaystyle="true" scriptlevel="0"\gt \lt mrow class="MJX-TeXAtom-ORD"\gt \lt mi mathvariant="bold"\gt v\lt /mi\gt \lt /mrow\gt \lt /mstyle\gt \lt /mrow\gt \lt annotation encoding="application/x-tex"\gt {\displaystyle \mathbf {v} }\lt /annotation\gt \lt /semantics\gt }[/math]<img alt="{\displaystyle \mathbf {v} }" aria-hidden="true" class="mwe-math-fallback-image-inline mw-invert" src="https://wikimedia.org/api/rest_v1/media/math/render/svg/35c1866e359fbfd2e0f606c725ba5cc37a5195d6" style="vertical-align: -0.338ex; width:1.411ex; height:1.676ex;"/> of the metal sheet. This force accelerates the electron giving it a component of velocity opposite to the sheet. Collisions of these electrons with the atoms of the sheet exert a drag force on the sheet.

| источник = Own work | время создания = 2020-11-21 | автор = Chetvorno — Лицензия: CC0 (Creative Commons Zero, Public Domain Dedication) http://creativecommons.org/publicdomain/zero/1.0/deed.en }} Источник файла — сайт Wikimedia Commons, куда он был загружен под одной из свободных лицензий ( https://commons.wikimedia.org/wiki/File:Eddy_currents_-_explanation_of_drag_force.svg ). Авторов, работавших над этим файлом см. в истории файла: https://commons.wikimedia.org/w/index.php?title=File:Eddy_currents_-_explanation_of_drag_force.svg&action=history

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