A capacitor having a capacitance of 100 μF is charged to a potential difference of 50 V.

A capacitor having a capacitance of $100 \mu \mathrm{F}$ is charged to a potential difference of $50 \mathrm{~V}$.

(a) What is the magnitude of the charge on each plate?

(b) The charging battery is disconnected and a dielectric of dielectric constant $2.5$ is inserted. Calculate the new potential difference between the plates,

(c) What charge would have produced this potential .difference in absence of the dielectric slab,

(d) Find the charge induced at a surface of the dielectric slab.