Could you please give a description of cavity theory and how to find the electric field in a cavity in the prescience of some charge in the cavity?

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