How to know how charges distribute themselves in parallel plate capacitors?How to start solving the questions.What concept to use and all?

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