An uncharged nonconductive hollow sphere of radius 18.0 cm surrounds a 12.0 µc charge located at the origin of a cartesian coordinate system. a drill with a radius of 1.00 mm is aligned along the z axis, and a hole is drilled in the sphere. calculate the electric flux through the hole.

10.36 N.m^2/C

Explanation: In order to calculate the electric flux through the hole drilled in the non conductive sphere which sorrounds a charge: Firstly we have to calculate the electric field at the radius of the sphere

To do that we have to use the Gaussian Law as:

∫E.dS= Total charge inside/ε0

E. Area= Qinside/ε0

E=Q/(4πR^2ε0)=3.3 10^6 N/C

After that we calculate the flux through the hole of 1 mm radius as follows:

E. Ahole= 3.3 10^6*π* (0,18)^2 =10.36 Nm^2/C