Question

# Two oppositely charged but otherwise identical conducting plates of area 2.50 square centimeters are separated by a dielectric 1.80 millimeters thick,

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Two oppositely charged but otherwise identical conducting plates of area 2.50 square centimeters are separated by a dielectric 1.80 millimeters thick, with a dielectric constant of K=3.60. The resultant electric field in the dielectric is $$\displaystyle{1.20}\times{10}^{{6}}$$ volts per meter.
Compute the magnitude of the charge per unit area $$\displaystyle\sigma$$ on the conducting plate.
$$\displaystyle\sigma={\frac{{{c}}}{{{m}^{{2}}}}}$$
Compute the magnitude of the charge per unit area $$\displaystyle\sigma_{{1}}$$ on the surfaces of the dielectric.
$$\displaystyle\sigma_{{1}}={\frac{{{c}}}{{{m}^{{2}}}}}$$
Find the total electric-field energy U stored in the capacitor.
u=J

a) the magnitude of the charge per unit area $$\displaystyle\sigma$$ on the conducting plate:
E effective=$$\displaystyle{\frac{{\sigma}}{{{k}\epsilon_{{0}}}}}$$
$$\displaystyle\sigma={3.6}\cdot{8.854}{e}^{{-{12}}}\cdot{1.20}{e}^{{6}}={3.82}\cdot{e}^{{-{5}}}{\frac{{{C}}}{{{m}^{{2}}}}}$$
$$\displaystyle\sigma$$ (on the dielectric) $$\displaystyle=\sigma{\left({\left({\frac{{{1}}}{{{k}}}}\right)}-{1}\right)}$$
$$\displaystyle=-{2.75}{e}^{{-{5}}}\ {\frac{{{C}}}{{{m}^{{2}}}}}$$