If a capacitor is connected to a battery why doesn’t a dielectric work?

I am asking this as there is a multiple correct of JEE Advanced 2014 that you might know.

So please clear my doubt

Electrostatics question based on earthing of spherical shell

an object has a charge of 2c and gains 10^19 electrons. the net chaarge on the object becomes??

A wire with a linear charge density lambda forms a quarter of a cjrclenof radius R and is placed asa shown in thefigure with its centre of curvature at the origin O the electric field at O will be

Find the value of q so that system remains in equilibrium.. figure attached below

Find the value of q so that system remains in equilibrium