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) \(\displaystyle=\sigma{\left({\left({\frac{{{1}}}{{{k}}}}\right)}-{1}\right)}\)

\(\displaystyle=-{2.75}{e}^{{-{5}}}\ {\frac{{{C}}}{{{m}^{{2}}}}}\)

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) \(\displaystyle=\sigma{\left({\left({\frac{{{1}}}{{{k}}}}\right)}-{1}\right)}\)

\(\displaystyle=-{2.75}{e}^{{-{5}}}\ {\frac{{{C}}}{{{m}^{{2}}}}}\)