Two large parallel plates are separated by a distance $d = 0.050 \, m$ and are charged with surface charge densities $\sigma_1 = +4.00 \, \mu C/m^2$ and $\sigma_2 = -2.00 \, \mu C/m^2$. The space between the plates is initially evacuated, but then it is filled with a dielectric material that has a dielectric constant $\kappa = 2.5$.
a) Calculate the electric field $E_0$ between the plates when the space is evacuated.
b) Determine the new electric field $E$ between the plates after the dielectric is introduced.
c) Calculate the potential difference $V$ between the plates with and without the dielectric.
d) If the dielectric is partially removed, leaving a thickness $d_1 = 0.030 \, m$ of dielectric and $d_2 = 0.020 \, m$ of vacuum, what is the new electric field $E_{new}$ in the space between the plates?