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- Homework Statement
- A capacitor consists of a pair of large parallel metal plates 3.0 mm apart, between which lies a parallel sheet of mica 2.5 mm thick; air fills the rest of the space between the plates. If the mica be taken to have a permittivity of 5, find the density of charge on the plates, and the voltage gradient in the air, when the capacitor is charged to a potential difference of 2000 V. If the mica is replaced by a pair of thin parallel metal sheets separated by 2.5 mm of air, find the density of charge needed on these sheets in order that the charge on the outer plates shall be the same as when the mica was in place; the potential difference of the capacitor being kept constant at 2000 V.

Answers: ##17.6\cdot 10^{-6} C/m^2;2.0MV/m;14.2\cdot 10^{-6}C/m^2##

- Relevant Equations
- $$C=\frac{Q}{V}=\frac{Q}{Q-q}\frac{\varepsilon _0S}{d}=\varepsilon_r\frac{\varepsilon_0S}{d}\Rightarrow \frac{Q}{S}=\frac{V\varepsilon_0\varepsilon_r}{d}=\frac{V\varepsilon}{d}$$

When I plug in the numbers I get ##2.9513\cdot 10^{-5}C/m^2##, not ##17.6\cdot 10^{-6} C/m^2##. Can someone point out where I'm going wrong?