# A large vessel is filled with a liquid. Two vertical plates touch the surface of the liquid. The dimensions of the plate are a and b, the distance between them is d. The plates have been charged by applying a voltage V and then disconnected form the voltage source. To what height will the liquid rise. (the density of liq is k) and what happens to height if voltage remains connected?

$forceontheliquid=\frac{{\left(CV\right)}^{2}}{2A{\epsilon}_{0}}=\frac{{\left(CV\right)}^{2}}{2ab{\epsilon}_{0}},A=ab\phantom{\rule{0ex}{0ex}}C=\frac{{\epsilon}_{0}ab}{d}\phantom{\rule{0ex}{0ex}}F=\frac{{\left(\frac{{\epsilon}_{0}abV}{d}\right)}^{2}}{2ab{\epsilon}_{0}}=\frac{ab{\epsilon}_{0}{V}^{2}}{2{d}^{2}}\phantom{\rule{0ex}{0ex}}lettherisebex\phantom{\rule{0ex}{0ex}}\frac{ab{\epsilon}_{0}{V}^{2}}{2{d}^{2}}=daxkg\phantom{\rule{0ex}{0ex}}\frac{b{\epsilon}_{0}{V}^{2}}{2{d}^{3}kg}=xistherise\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Regards\phantom{\rule{0ex}{0ex}}$

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