Question

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

Answer 1

a) the magnitude of the charge per unit area \(\displaystyle\sigma\) on the conducting plate:
E effective=\(\displaystyle{\frac{{\sigma}}{{{k}\epsilon_{{0}}}}}\)
\(\displaystyle\sigma={3.6}\cdot{8.854}{e}^{{-{12}}}\cdot{1.20}{e}^{{6}}={3.82}\cdot{e}^{{-{5}}}{\frac{{{C}}}{{{m}^{{2}}}}}\)
b) The magnitude of the charge per unit area σ1 on the surfaces of the dielectric.
\(\displaystyle\sigma\) (on the dielectric) \(\displaystyle=\sigma{\left({\left({\frac{{{1}}}{{{k}}}}\right)}-{1}\right)}\)
\(\displaystyle=-{2.75}{e}^{{-{5}}}\ {\frac{{{C}}}{{{m}^{{2}}}}}\)