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Merge pull request #6 from VikParuchuri/dev
Fix image resizing, py3.9
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The potential $V_{i}$ of cell $\mathcal{C}_ {j}$ centred at position $\mathbf{r}_ {i}$ is related to the surface charge densities $\sigma_ {j}$ of cells $\mathcal{E}_ {j}$ $j\in[1,N]$ through the superposition principle as: | ||
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$$V_ {i}\,=\,\sum_ {j=0}^{N}\,\frac{\sigma_ {j}}{4\pi\varepsilon_ {0}}\,\int_{\mathcal{E}_ {j}}\frac{1}{\left|\mathbf{r}_ {i}-\mathbf{r}^{\prime}\right|}\,\mathrm{d}^{2}\mathbf{r}^{\prime}\,=\,\sum_{j=0}^{N}\,Q_ {ij}\,\sigma_{j},$$ | ||
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where the integral over the surface of cell $\mathcal{C}_ {j}$ only depends on $\mathcal{C}{j}$ shape and on the relative position of the target point $\mathbf{r}_ {i}$ with respect to $\mathcal{C}_ {j}$ location, as $\sigma_ {j}$ is assumed constant over the whole surface of cell $\mathcal{C}_ {j}$. | ||
The potential $V_ i$ of cell $\mathcal{C}_ i$ centred at position $\mathbf{r}_ i$ is related to the surface charge densities $\sigma_ j$ of cells $\mathcal{C}_ j$ $j\in[1,N]$ through the superposition principle as: $$V_ i = \sum_ {j=0}^{N} \frac{\sigma_ j}{4\pi\varepsilon_ 0} \int_ {\mathcal{C}_ j} \frac{1}{|\mathbf{r}_ i-\mathbf{r}'|} \mathrm{d}^2\mathbf{r}' = \sum_{j=0}^{N} Q_ {ij} \sigma_ j,$$ where the integral over the surface of cell $\mathcal{C}_ j$ only depends on $\mathcal{C}_ j$ shape and on the relative position of the target point $\mathbf{r}_ i$ with respect to $\mathcal{C}_ j$ location, as $\sigma_ j$ is assumed constant over the whole surface of cell $\mathcal{C}_ j$. |
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