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\documentclass[12pt]{article}
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\pagestyle{empty}
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\begin{document}
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\begin{eqnarray*}
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E & = & \frac{Cq_iq_j}{\epsilon r} \left( \frac{\epsilon}{\epsilon_D(r)}-1\right) \qquad r < r_c \\
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\epsilon_D(r) & = & \frac{5.2+\epsilon}{2} + \frac{\epsilon-5.2}{2}\tanh\left(\frac{r-r_{me}}{\sigma_e}\right)
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\end{eqnarray*}
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\end{document}
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\documentclass[12pt]{article}
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\pagestyle{empty}
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\begin{document}
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\begin{eqnarray*}
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E = & \frac{H}{\sigma_h\sqrt{2\pi}} \exp\left[-\frac{(r-r_{mh})^2}{2\sigma_h^2}\right]
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\end{eqnarray*}
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\end{document}
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