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.

Answer: 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