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Both sides previous revision Previous revision Next revision | Previous revisionLast revisionBoth sides next revision | ||
184_notes:examples:week5_flux_cylinder [2017/09/24 18:57] – [Solution] tallpaul | 184_notes:examples:week5_flux_cylinder [2017/09/24 18:59] – [Solution] tallpaul | ||
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Each little piece will have a " | Each little piece will have a " | ||
- | $$\Phi_1 = \vec{E}\bullet\vec{A}_1 = E\hat{x}\bullet\vec{A}_1 = E\cdot(\hat{x}\bullet\vec{A}_1) = E\cdot(\hat{x}\bullet-\vec{A}_2)$$ | + | $$\Phi_{A_1} |
- | Within the sum, we can match up the little pieces of area with their opposites (like $\vec{A}_1$ and $\vec{A}_2$ in the figure). | + | It shouldn' |
- | $$\Phi_{\text{matching pieces}}=\Phi_{A_1}+\Phi_{A_2} | + | $$\Phi_{\text{matching pieces}}=\Phi_{A_1}+\Phi_{A_2} = 0$$ |
We can continue in the manner for the entire wall, and we will find that | We can continue in the manner for the entire wall, and we will find that | ||
$$\Phi_{\text{wall}}=0$$ | $$\Phi_{\text{wall}}=0$$ | ||
In total, | In total, | ||
$$\Phi_{\text{cylinder}}=\Phi_{\text{top}}+\Phi_{\text{bottom}}+\Phi_{\text{wall}}=0$$ | $$\Phi_{\text{cylinder}}=\Phi_{\text{top}}+\Phi_{\text{bottom}}+\Phi_{\text{wall}}=0$$ |